Summary: In this paper, we consider the least-square solutions \({X^*} \in {\mathbb{R}^{p \times q}}\) of the matrix equations \(AX = B, XC = D\) with respect to the semi-tensor product, where matrices \(A \in {\mathbb{R}^{m \times n}}, B \in {\mathbb{R}^{h \times k}}, C \in {\mathbb{R}^{a \times b}}, D \in {\mathbb{R}^{l \times d}}\) are given. By using the definition of the semi-tensor product, we transform the original problem under semi-tensor product into some related matrix least squares with the conventional matrix product. Then, combining with the differentiation and singular value decomposition of matrices, we give the explicit representation of the least squares solution. Finally, we present some elementary numerical examples to verify the proposed results.