In this paper, we obtain a variational principle for the new coupled Zakharov-Kuznetsov (ZK) system by the semi-inverse method. Based on this formulation, a new solitary wave solution can be easily obtained using Ritz method. We obtained the conditions which must remain valid for continuation of the new solitary solution and other solutions to exist. We also studied the collision dynamics between waves in each case. Finally, we give the numerical simulations to complete the study. (C) 2015 Elsevier Ltd. All rights reserved.