A new 3-D diffusion code using a recently published layer method has been developed to analyze radiation belt electron dynamics. The code guarantees the positivity of the solution even when mixed diffusion terms are included. Unlike most of the previous codes, our 3-D code is developed directly in equatorial pitch angle (α0), momentum (p), and L shell coordinates; this eliminates the need to transform back and forth between (α0,p) coordinates and adiabatic invariant coordinates. Using (α0,p,L) is also convenient for direct comparison with satellite data. The new code has been validated by various numerical tests, and we apply the 3-D code to model the rapid electron flux enhancement following the geomagnetic storm on 17 March 2013, which is one of the Geospace Environment Modeling Focus Group challenge events. An event-specific global chorus wave model, an AL-dependent statistical plasmaspheric hiss wave model, and a recently published radial diffusion coefficient formula from Time History of Events and Macroscale Interactions during Substorms (THEMIS) statistics are used. The simulation results show good agreement with satellite observations, in general, supporting the scenario that the rapid enhancement of radiation belt electron flux for this event results from an increased level of the seed population by radial diffusion, with subsequent acceleration by chorus waves. Our results prove that the layer method can be readily used to model global radiation belt dynamics in three dimensions.