This talk establishes a quantum cluster algebra structure on the multi-parameter quantum coordinate ring M_{p,u} of generic matrices. Following the framework of multi-parameter quantum cluster algebras developed by Goodearl and Yakimov,  we first recall the basic notions of based quantum tori, toric frames, quantum seeds, and their mutations. we prove that M_{p,u} is a symmetric CGL extension and hence a quantum nilpotent algebra, equipped with a natural torus action. By using the homogeneous prime elements of M_{p,u}, we construct a toric frame and an exchange matrix B, and prove that the pair (B,r) is compatible. Consequently, the multi- parameter quantum coordinate ring M_{p,u} carries a natural quantum cluster structure, and is contained in the corresponding upper quantum cluster algebra. This work extends the cluster theory to the multi-parameter quantum matrix case and provides new examples of quantum nilpotent algebras with explicit cluster structures.