Numerical simulation is used to calculate accurately the electrophoretic mobility of a charged spherical nanoparticle confined in a nanochannel, under a weakly applied electric field. Classic models or electrophoretic mobility are valid only in the linear regime of small particle zeta potential, and for an unbounded fluid domain. However, these models fail to predict the electrophoretic mobility measured experimentally in bounded nanochannels. We adopt asymptotically expanded formulations and solve the fully coupled equations on a 3D finite element domain. Factors affecting particle mobility include electrolyte concentration, channel size, and zeta potentials on both the particle surface and channel walls. Specifically, spherical particles are examined with diameters 2a = 10 and 50 nm, in a 100 nm high channel. The non-dimensionalelectric double layers were varied between 0.1 < κa < 100. The results indicate that the mobility of a particle located at the nanochannel centerline agrees to within 1% of the average mobility of a particle distributed transversely throughout the nanochannel. Furthermore, confinement by the nanochannel walls was found to affect greatly nanoparticle mobility. As a result, it is feasible to use nanochannels to separate two different size nanoparticles, even when the particles have equal zeta potentials. Finally, a new method is proposed to estimate accurately particle and wall zeta potentials by contrasting the observed differences in mobility between observed in two different height channels.