We characterize the performance of the optical signal propagation model of multi-level pulse amplitude modulation (M-PAM) based on avalanche photodiode (APD) detector in the free-space link for the first time. When the number of photons absorbed by the active surface of the APD is large enough, the bit error rate (BER) performance relationship of the systems based on the signal intensity and the photon characteristics are depicted. We use the Gamma-Gamma (G-G) channel model to analysis the communication systems with joint parameter constraints, and demonstrate the atmospheric turbulence intensity, link lengths, optical wavelength, symbol transmission rate, temperature of APD and pointing errors (PEs) impact on the system average bit error rate (ABER) performance. Moreover, the relationship between signal-to-noise-ratio (SNR) and ABER rate is given. The numerical results show that the 4-PAM free-space optical (FSO) communication is suitable for medium-to-weak turbulence, and the high gain of APD can mitigate the influence of ABER. The best detection condition of the 4-PAM optical signal is at least 20 dB SNR, when the ABER is under the 7% forward error correction (FEC) limit of 3.8 × 10-3. This work provides a reference for parameter designing and evaluating in M-PAM FSO communication systems.