This paper is devoted to a new neural particle method (NPM) based on physics-informed neural networks (PINNs) for modeling free surface flows. Utilizing interface tracking techniques and machine learning (ML) modeling, the new NPM approach with interface tracking and adaptive particle refinement (NPM-LA) is suggested. This method encompasses properties of tracking the interface particles and ensuring the preservation of the designated distribution pattern for interior fluid (computational) particles. The determination of the corresponding physical quantities at these particles is accomplished through the process of inference, a distinctive feature facilitated by ML. The proposed NPM-LA effectively provides solutions for both appropriately tracking the morphology of complex flow surfaces and enhancing the accuracy by dynamically redistributing particles into desired patterns within the computational domain. Two testing cases (the 2D Poiseuille flow problem and a rotating square patch of inviscid fluid) are adopted to examine the performance of the proposed NPM-LA method. The applications to experiments of dam break and wave breaking problems are explored for demonstrating the capability of capturing the complex deforming flow surface.