In this article, the homogeneous balance method is used to construct exact traveling wave solutions for the modified Zakharov–Kuznetsov equation using the Riccati equation. This method is a powerful tool for obtaining exact traveling wave solutions of nonlinear evolution equation. Many exact traveling wave solutions of nonlinear modified Zakharov–Kuznetsov equation are constructed which contain soliton and periodic solutions. The results reveal that the method is very effective and simple.