In this paper, a simple and robust multi-dimensional shock-capturing limiter is presented and applied to the high-order least square-based finite difference-finite volume (LSFD-FV) method for simulation of compressible inviscid flows on unstructured grids. The novel limiter considers all the spatial information of the neighbouring supporting cells of the reference cell instead of only the immediate neighbours. As a result, the local upper and lower bounds can be correctly defined based on the extrema at specific points within the supporting stencil and thereafter the numerical oscillations in the adjacent region to the discontinuities can be suppressed effectively. The main advantage of this limiting technique lies in its simple methodology and easy implementation. Furthermore, the multi-dimensional character and the point extrema-based methodology endow the proposed limiter with ability to solve multi-dimensional flow problems on unstructured grids. A series of smooth and non-smooth numerical examples in one, two and three dimensions on unstructured grids are tested. Numerical results obtained demonstrate the superior performance of the proposed limiter on simulating compressible inviscid flows.