For enabling image enlargement or reduction of high image quality with improved definition, there is disclosed an image interpolating device comprising a memory for storing digital image signal, memory readout means for reading pixel data in succession from the memory, first, second and third consecutive delay means for respectively delaying the image signal S.sub.n, read by the memory readout means, to respectively from pixel signals S.sub.n-1, S.sub.n-2, S.sub.n-3, first, second, third and fourth coefficient generation circuits for generating interpolation coefficients respectively corresponding to the pixel signals S.sub.n, S.sub.n-1, S.sub.n-2, S.sub.n-3 and determined by N-th order functions from the position of the interpolated pixel S' positioned between the pixel signals S.sub.n-1 and S.sub.n-2, and a signal synthesis circuit for calculating the sum of respective product of pixel signal S.sub.n and interpolation coefficient k.sub.n.