Frequency stabilized lasers are very important in many fields such as precision metrology and high resolution spectroscopy. A Nd:YAG laser (1064 nm) frequency stabilization scheme is reported. In this scheme, the laser frequency is doubled and stabilized at the R(56) absorption line of (32-0) band in the B-X system of molecular iodine based on digital proportion-integration-differentiation (PID) technique. The frequency stability reaches 10-9 and the frequency drift is less than 2 MHz in 1 h, which is far less than the Doppler-limited molecular absorption linewidth. This scheme can suppress the laser frequency drift effectively and minimize the large-amplitude random noise. It is proved simple and easy to implement.