Using the renormalization-group transformation and cumulant expansion technique, the Gaussian model with two-spin interactions and triplet-spin interactions on the Sierpinski gasket lattice is studied, and its fixed points and critical exponents are obtained. Compared with the case of only two-spin interactions, the fixed points and critical exponents have changed. The results show that the fixed points and critical exponents are all dependent on triplet-spin interactions in the cases with or without external field.