We propose a method for multi-pass non-collinear optical parametric chirped pulse amplification (MNOPCPA) based on two geometries, tangent phase-matching (TPM) and Poynting vector walk-off compensation (PVWC), which optimize the performance of optical parametric chirped pulse amplification (OPCPA). A feasible design scheme is also presented for use in implementing this approach. Employing this design, we construct and perform a numerical simulation, showing that back-conversion from the signal and idler to the pump can be inhibited, and that the conversion efficiency can be boosted dramatically, approaching the theoretical limit of ~64%, when amplification is nearly saturated at full bandwidth. In the MNOPCPA scheme, the output signal has a wider spectrum and a corresponding shorter Fourier-limited pulse duration with the pump being continuously depleted. A barycenter shift of the signal spot results from a spatial walk-off effect due to the pump, which can be offset and corrected well. To the best of our knowledge, this is the first demonstration of a multi-pass non-collinear OPCPA method employed the scheme of regenerative amplification.