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This paper proposes a novel three-dimensional (3D) two-sphere regular-shaped geometry-based stochastic model (RS-GBSM) with only double-bounced rays for non-isotropic scattering narrowband multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) channels. The proposed 3D model has the ability to investigate the joint impact of both the azimuth angle and elevation angle on channel statistics. Based on the proposed model, the space-time (ST) correlation function (CF) is derived and the impact of some important parameters on the resulting ST CF is investigated. Numerical results show that the 3D model results in lower ST correlations than the corresponding 2D model.