The Finite Volume Particle Method (FVPM) is a meshless method for simulating fluid flows which includes many of the desirable features of mesh-based finite volume methods. In this paper, we develop a new 3-D FVPM formulation that features spherical kernel supports. The formulation is based on exact integration of interaction vectors constructed from top-hat kernels. The exact integration is obtained by an innovative surface partitioning algorithm as well as precise area computation of the sphere subsurfaces. Spherical-support FVPM improves the recently developed cubic-support version in two main aspects: spherical kernels have no directionality and result in smooth interactions between particles, leading to an improved method. We present three test cases that illustrate the improved accuracy and robustness brought by the spherical kernel. Although computations are 1.5 times slower on spherical support than cubic support, the cost is more than compensated by lower error with a higher convergence rate. (C) 2016 Elsevier B. V. All rights reserved.