For underwater acoustic communication, pilot pattern optimization is usually investigated to improve the performance of channel estimation based on compressed sensing (CS) in orthogonal frequency division multiplexing (OFDM) systems. However, there is no deterministic criteria to design a perfect pilot pattern utilizing the measurement matrix, and no mature methods to quantitatively measure the relationship between the influence indicators and estimation performance of pilot patterns. An analytical method with grey correlation degree is proposed to try to solve the problem. The influence indicators are weighted with information entropy and the grey correlation degrees of various optimization strategies are calculated. Experimental results demonstrate the proposed method is intuitive and effective, due to the order of the grey correlation degrees entirely consists with the order of the channel estimation performance on bit error rate (BER) and mean square error (MSE). Moreover, it is indicated that the ratio of large off-diagonal entries in the Gram matrix has a greater impact on the performance of channel estimation compared to the minimal mutual coherence, the ratio of small off-diagonal entries, and the ratio of middle off-diagonal entries.