In this paper, we utilize the sine-Gordon expansion method and construct some travelling wave solutions to the (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsev equation which arises in plasma physics. We successfully obtain some hyperbolic function solutions to this equation. By choosing some suitable values of parameters, we perform the numerical simulation of all the obtained solutions in this study. We observed that our result may be useful in detecting some ion-acoustic waves behaviors in a magnetized plasma. All the computations and graphic plots in this article are performed with the aid of the Mathematica package.