There are same occasions to extract the moving object from image sequence in the region of remote sensing, robot vision and so on. The process needs to have high accurate extraction and simpler realization. In this paper, we propose the design method of the optimal filter in the frequency-time mixed domain. Frequency selective filter to dynamic images usually are designed in 3-D frequency domain. But, design method of the filter is difficult because of its high parameter degree. By the use of frequency-time mixed domain(MixeD) which constitutes of 2-D frequency domain and 1-D time domain, design of filters becomes easier. But usually the desired and noise frequency component of image tend to concentrate near the origin in the frequency domain. Therefore, conventional frequency selective filters are difficult to distinguish these. We propose the optimal filter in the MixeD in the sense of least mean square error. First of all, we apply 2-D spatial Fourier to dynamic images, and at each point in 2-D frequency domain, designed FIR filtering is applied to 1-D time signal. In designing the optimal filter, we use the following information to decide the characteristics of the optimal filter. (1) The number of finite frames of input images. (2) The velocity vector of the signal desired. (3) The power spectrum of the noise signal. Signals constructed by these information are applied for the evaluation function and it decides filter coefficients. After filtering, 2-D inverse Fourier transform is applied to obtain the extracted image.