A polar-coded orthogonal frequency-division multiplexing (OFDM) underwater acoustic communication system was developed, and a Monte Carlo (MC) method for constructing optimal polar codes was proposed to improve the performance of the system in this study. Several optimal polar codes with different code lengths and rates were constructed for a shallow-water acoustic channel. Simulations showed that the polar codes constructed using the MC method rendered superior performance than those constructed using the Bhattacharyya parameter and the Gaussian approximation method. In addition, shallow-water acoustic communication experiments were conducted at Xiamen port. The results show that the developed polar-coded OFDM communication system has excellent performance with 196 out of 200 frames achieving error-free transmission, which is much greater than the performance (157 out of 200) of the LDPC-coded OFDM communication system.