There are 69 known moons of Jupiter. This gives Jupiter the largest number of moons with reasonably stable orbits of any planet in the Solar System. The most massive of the moons are the four Galilean moons, which were independently discovered in 1610 by Galileo Galilei and Simon Marius and were the first objects found to orbit a body that was neither Earth nor the Sun. From the end of the 19th century, dozens of much smaller Jovian moons have been discovered and have received the names of lovers or daughters of the Roman god Jupiter or his Greek equivalent Zeus.

69 moons name of Jupiter.

1. Metis
2. Adrastea
3. Amalthea
4. Thebe
5. Io
6. Europa
7. Ganymede
8. Callisto
9. Themisto
10. Leda
11. Himalia
12. Lysithea
13. Elara
14. Dia
15. Carpo
16. S/2003 J 12
17. Euporie
18. S/2003 J 3
19. S/2011 J 1
20. S/2003 J 18
21. S/2010 J 2
22. Thelxinoe
23. Euanthe
24. Helike
25. Orthosie
26. S/2016 J 1
27. Iocaste
28. S/2003 J 16
29. Praxidike
30. Harpalyke
31. Mneme
32. Hermippe
33. Thyone
34. Ananke
35. Herse
36. Aitne
37. Kale
38. Taygete
39. S/2003 J 19
40. Chaldene
41. S/2003 J 15
42. S/2003 J 10
43. S/2003 J 23
44. Erinome
45. Aoede
46. Kallichore
47. Kalyke
48. Carme
49. Callirrhoe
50. Eurydome
51. Pasithee
52. S/2010 J 1
53. Kore
54. Cyllene
55. S/2011 J 2
56. Eukelade
57. S/2017 J 1
58. S/2003 J 4
59. Pasiphae
60. Hegemone
61. Arche
62. Isonoe
63. S/2003 J 9
64. S/2003 J 5
65. Sinope
66. Sponde
67. Autonoe
68. Megaclite
69. S/2003 J 2

Thanks for your questions. If you have more questions, ask me.

Lately, this question has had a changing answer! For many years, we knew of 16 moons for the largest planet in our solar system. In the last few years, about two dozen new moons have been announced by astronomers. However, being announced does not mean that these become “official” moons of the planet. To be recognized by the scientific community as a new moon involves a process which may take several years – and some announced objects never get recognized at all! Let’s explain.

When a scientist makes observations which indicate a new moon, they submit their data and analysis to the scientific community. Other scientists then try to confirm the existance of the new moon by additional observations. If it is confirmed, the data are all submitted to the International Astronomical Union (IAU). The IAU is the governing body for astronomy. One of their jobs is to decide what is sufficiently proven and what is not, and then to assign names. If sufficiently confirmed, the IAU gives a preliminary name to the new moon. Scientists get time to consider the name. Finally, at one of their meetings, the scientific membership of the IAU votes on whether or not to accept the object and its name as an “official moon” of the planet. This process (from initial announcement to official acceptance) may take several years.

Of the 23 new moons announced for Jupiter, preliminary names were assigned to 11 of them by the IAU in October 2002. This is an important step in the path taken to become an “official” moon. So these 11 (which are most probably asteroids that have been captured by Jupiter’s gravity) will most probably be accepted in the near future and take the official list of Jupiter’s moons from 16 to 27. How many more will follow this course is something to stay tuned for!

By the way, the recently proposed new moon names are: Themisto, Iocaste, Harpalyke, Praxidike, Taygete, Chaldene, Kalyke, Callirrhoe, Megaclite, Isonoe, and Erinsome. These names are from characters in the life of Zeus or Jupiter in Greco-Roman mythology, thus following in the tradition of the other satellites of our largest planet.

UPDATE! As of January 2009, Jupiter has 49 official, named moons and 14 more unofficial ones still under consideration..

Answer Source: NASA Website