<p>Liquid sloshing phenomenon refers to a kind of wave motion inside a partially filled tank. In this article, a mesh-free method based on exponential basis functions (EBFs) is proposed in order to analyze the liquid sloshing phenomenon in a two-dimensional rectangular tank. This method is a boundary-type mesh-free method applying the exponential basis functions with complex exponents. The solution of governing equations is considered as a series of these basis functions. Boundary conditions are met through a point-wise collocation approach. In this method, the velocity potential equation is applied in the Mixed Eulerian–Lagrangian (MEL) form. The results obtained by this numerical method with respect to sloshing problems are verified through comparisons with experimental data and analytical findings. The results here indicated the ability of this numerical method in simulating free surface flow problems like sloshing phenomenon with good accuracy, convenient performances and the least run time calculation. The mesh-free numerical method presented in this paper can solve small and large amplitude sloshing problems through a time marching with larger time increments and good stability.</p>