The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian distribution constants b and bw is constructed by generalizing that on a translationally invariant square lattice. The critical behaviours are studied by the renormalization-group approach and spin rescaling method. They are found to be quite different from that on a translationally invariant square lattice. There are two critical points at (K* = b, K*w = 0) and (K* = 0, K*w = bw), and the correlation length critical exponents are calculated.