A motion vector computing device according to one embodiment includes: a difference computing unit that computes inter-frame temporal difference value It, uses horizontal direction inter-pixel difference value Ix and vertical direction inter-pixel difference value Iy in a same frame, the current frame signal and the different frame signals when the pixel moves for a small-time, a variance matrix generating unit computes the variances of the gradient in the horizontal direction, in the vertical direction and in the temporal direction of the luminance value on the basis of the difference values Ix, Iy and It, a coefficient computing unit computes a coefficient of a flat plane formula by calculating a formula for giving a minimum with regard to the square error of the flat plane formula approximating the distribution of luminance gradients of the pixel and a vector computing unit computes the motion vector uses the coefficient.