Iodine-stabilization lasers are becoming important wavelength standards and optical frequency standards. The frequency value of Iodine R (56) 32-0 transition was recommended as the standard frequency for practical realization of the meter by CIPM in 2001. Molecular iodine has rich strong absorption lines near 532 nm that can provide the absolute references for frequency stabilization. A monolith solid laser was tuned at the spectrum of transition R (56) 32-0 of iodine molecule with new modulation frequency 375 kHz. And 15 hyperfine components of this spectrum were observed using modulation transfer spectroscopy. The sensitivity of frequency detecting with 375 kHz modulation frequency was higher than that with 312 kHz modulation frequency by broadening one hyperfine component. The laser frequency was successfully locked at a10 component for no less than 10 hours. The frequency stability was estimated about level of 10-13, and the exact value of frequency stability is under measurement by frequency beating between two same kind of lasers.