In this letter, we demonstrated a Mach-Zehnder interferometer-type photonic switch using multimode interference (MMI) couplers with InAlGaAs-InAlAs compound semiconductor materials. A hybrid-waveguide structure with different etching depths was adopted for MMI couplers and other parts of the waveguides for polarization-independent operation. As a result, low-crosstalk switching operation of less than -20 dB was confirmed regardless of polarizations of an input light. Switching currents were, respectively, 5.25 and 4.75 mA for TE and TM modes of the input light. High-speed switching operation with about 3-ns transition time was also confirmed.