The basic goal is to investigate general convexity of multidimensional functions and derive several important inequalities associated with it's in this paper. For this reason, multidimensional general convex functions were firstly defined. Afterwards, some properties of these functions were mentioned. Accordingly, the relation of multidimensional general convex functions with other convex functions was established. Additionally, a generalization of Hermite-Hadamard type integral inequality was showed for two-dimensional general convex functions. Finally, Hermite-Hadamard type integral inequality for multidimensional general convex functions was verified and an explanatory example for this inequality was given in this study.