In this paper, a generalized variable-coefficient Boiti-Leon-Pempinlli (BLP) system is studied via the modified Clarkson and Kruskal (CK) direct reduction method connected with homogeneous balance (HB) method, which can describe the water waves in fluid physics. A direct similarity reduction to nonlinear ordinary differential system is obtained. By solving the reduced ordinary differential system, new analytical solutions (including solitary and periodic types) in terms of Jacobi elliptic functions are given for the variable coefficient BLP system. (C) 2017 Elsevier Ltd. All rights reserved.