Here's my June 2015 list that includes in service, launched, and building...it could be updated for the latest of each:
CV : 1
001 Liaoning: 1
001A (building - possibly)
LPD : 3
071 : 3 (1 more launched)
LST + 4000 t : 28
072A : 10 (2 more launched)
072 I : 3
072 II : 4
072 III : 11
DDG : 24
052D : 1 (5 more launched, 3 more building)
052C : 6
052B : 2
052 : 2
051D : 2
051G1/2/DT : 4
051C : 2
051B :1
Project 956/EM : 2/2
FFG :52
054 : 2
054A : 19 (5 more launched)
053H3 : 10
053H2G : 4
053H : 3
053H1 :6
053H2 : 1
053H1Q : 1
053H1G : 6
Corvettes : 120
056 : 22 (3 more launched, 2 more building)
037 II : 6
037 IG : 24
037/IS : about 68
Missile boats :60
022 : 60
SSBN/SSN : 8/9
094 : 3 or 4
093 : 2
091 : 3
SSK : 52
039/G/G1 : 16
039A/B : 12/13
Project 877/636/636M : 12
035 : 12
Combat support ships, large : 7
903 : 4 (3 more launched)
905 : 2
908 : 1
Minesweepers : about 38
That's a total of 438 vessels of all types (with 19 more already launched and more building)