A high-performance InAlAs avalanche photodiode (APD) with a vertical-illumination structure for 50-Gbit/s applications is presented. The vertical-illumination structure we employed is advantageous for large optical tolerance and thus enables easier optical coupling than waveguide structures. Although the vertical illumination structure generally has disadvantages in terms of both responsivity and bandwidth, our fabricated APD exhibits a high responsivity of 0.69 A/W with a large 3-dB bandwidth of over 30 GHz at a multiplication factor (M) of 4.6 and a large gain-bandwidth product of 270 GHz, thanks to an unique hybrid absorption layer of p-doped/undoped InGaAs and a thin InAlAs avalanche layer. Furthermore, an optical receiver assembled with the APD and a trans-impedance amplifier (TIA) successfully demonstrates 50-Gbit/s error-free operation for the first time. The receiver sensitivity of -10.8 dBm at a BER of 10-12 is obtained against non-return-to-zero optical input signals at a wavelength of 1310 nm. In these operating conditions, the power consumption of the APD receiver module is less than 500 mW, where more than 98 % of the power is consumed by the TIA. The obtained minimum receiver sensitivity is enough for 20-km transmission at 50 Gbit/s when we assume a launch power of 0 dBm and transmission loss in the optical fiber of 0.5 dB/km. These results indicate our APD is promising for the systems with a serial baud rate of 50 Gbit/s such as 400-Gbit/s Ethernet systems.