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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. FVPM benefits from particle interaction vectors to weight conservative fluxes exchanged between particles. These vectors are equivalent to the intercell area vectors in mesh-based finite volume methods. To compute the interaction vectors, either numerical or exact integration has been used. Numerical integration, based on quadrature rules, is approximate and costly, whereas the exact method, employing a top-hat kernel, is precise and fast. To date, quadrature integration has not been used in 3-D due to its excessive cost and the exact method has been developed only for 2-D computations. In this study, we develop a new 3-D FVPM formulation which features a rectangular top-hat kernel to compute interaction vectors exactly and efficiently. We also introduce a new boundary condition enforcement technique based on a single layer of boundary particles. In this technique, no-slip wall boundary conditions with complex geometries are precisely enforced by overlaying a layer of particles on wall surfaces. Employing AUSM+ for inviscid fluxes, weakly-compressible fluid flow is studied with the proposed method. To achieve more accurate results, the solution can be refined near the wall boundary by splitting the fluid particles. This formulation is validated for lid-driven cavity flow, a moving square and jet impingement test cases.