To satisfy the strict requirements of semiconductor lasers in terms of wavelength stability, phase noise, and other indicators in precision measurements and similar applications, an analysis method based on the combination of system transfer function theory derivation analysis and simulation verification is proposed. We designed a semiconductor laser diode drive circuit with a smaller wavelength drift and ultra-low noise. For an alternating current small-signal model and alternating current path, we theoretically analyzed the correlation between the circuit parameters and system stability. The circuit design was optimized by introducing a noise-suppression network. Using Tina-TI simulations, the drive circuit loop noise is effectively suppressed, and the system stability improves to a bandwidth below 2 MHz. Experimental results reveal that the effective value of alternating current noise is approximately 224 nA and 1.9×10^-6 for the direct current ripple between 3 kHz and 2 MHz in 2.5 h. When the 1 h optical power integration time is 1 s, the stability is 1.177×10^-5. These results verify the theoretical model and simulation analysis. Notably, this approach provides a universal guideline for analyzing and designing ultra-low noise current drivers for semiconductor laser diodes.