In this paper, we introduce the definition of the generalized reduced biquaternions and propose a real representation of a generalized reduced biquaternion matrix. By using the matrix representation, we discuss the least-squares problems of the classic generalized reduced biquaternion matrix equation $AXC=B$. The least-squares solution to the above matrix equation is formulated by a least-squares real solution of its corresponding real matrix equation. Furthermore, two numerical examples are given to illustrate our results.