There exist a wide range of applications for solutions to multiphase flow problems with moving interfacial dynamics. These include engineering, fluid mechanics, melting metals, geophysical, medical, computer graphics and image processing. Over the years there have been a large effort in the numerical method community to solve these types of problems. Capturing topological changes with physical accuracy remains a challenge. The two main computational approaches for simulating moving interfaces can be categorized as interface capturing (most notably volume of fluid (VOF) and the level set method) and interface tracking methods. The advantages of both kinds of methods can be combined using hybrid methods, such as the particle level set method. In this paper we propose a new particle level set method which uses an interpolation scheme to update the radii of the interface particles. Preliminary results show that this method can outperform the original particle level set method using fewer particles.