To reduce the atmospheric turbulence-induced power loss, an AlexNet-based convolutional neural network (CNN) for wavefront aberration compensation is experimentally investigated for free-space optical (FSO) communication systems with standard single mode fiber-pigtailed photodiodes. The wavefront aberration is statistically constructed to mimic the received light beams with the Zernike mode-based theory for the Kolmogorov turbulence. By analyzing impacts of CNN structures, quantization resolution/noise, and mode count on the power penalty, the AlexNet-based CNN with 8 bit resolution is identified for experimental study. Experimental results indicate that the average power penalty decreases to 1.8 dB from 12.4 dB in the strong turbulence.