In this paper, a modulation transfer spectroscopy (MTS) of the hyperfine components at R67(15-1) transition of the iodine molecule is obtained with a 583 nm semiconductor frequency-doubling laser. For frequency stabilization of cooling laser in ultracold erbium experiment, the Pound-Drever-Hall (PDH) technique is used as the prefeedback to stabilize the laser to a Fabry-Perot cavity, and the MTS of iodine molecular is used as the secondary feedback to overcome the inevitable long-term drift of the optical reference cavity. The long-term drift data during 4 h show that, compared with the drift in frequency stabilization using only PDH technique (205 kHz), the maximum frequency fluctuation is within ±12 kHz for the two-stage laser stabilization. This meets the long-term stable operation requirements of the ultracold erbium atomic experimental system. The scheme expands the application of iodine molecular spectroscopy in 583 nm laser frequency stabilization, and provides a strategy for laser stabilization of cooling light in cold atom experiment with elements such as europium and thulium.