AbstractThe finite‐difference method has been widely utilized in seismic wave numerical modeling, seismic imaging, and full waveform inversion; the accuracy of finite‐difference numerical solution directly affects the result of seismic imaging and inversion. We can truncate spatial convolutional counterpart of the pseudo‐spectral method to get finite‐difference operators using truncated windows, and the properties of truncated windows in their amplitude responses play a major role in finite‐difference approximation. In specific, the accuracy of finite‐difference approximation can be determined by the properties of main lobe and side lobe in the amplitude response of window functions, narrower main lobe and larger attenuation of side lobe bring higher accuracy of finite‐difference approximation, and significantly suppress numerical dispersion. According to it, we propose an optimized method based on Chebyshev auto‐convolution combined window function which has narrow main lobe and large attenuation of side lobe. Through adjusting three parameters of the Chebyshev auto‐convolution combined window function, we visually and more intuitively control the properties of main lobe and side lobe to adjust the accuracy of finite‐difference approximation. The optimized explicit finite‐difference operator increases the accurate wave number coverage range and reduces the volatility of accuracy error, which indicates that the accuracy of low‐order operators can reach that of high‐order operators. In respect of economics, it effectively reduces the computational cost and improves the computational efficiency.