Recently, the concepts of dynamic phasors and shifted-frequency analysis (SFA) have received renewed attention as a possible solution framework for the modeling of power system components and transients, as opposed to using instantaneous time-domain variables or conventional phasors. In this paper, a new voltage-behind-reactance (VBR) synchronous machine model based on SFA is presented. Using dynamic phasors, the proposed model permits the use of a much larger range of step sizes to efficiently simulate electromagnetic and electromechanical transients. Moreover, the proposed model has a constant-parameter (CP) stator interface, which is simple to implement and numerically more efficient compared with the prior state-of-the-art models with rotor-position-dependent stator inductance matrices. Rigorous transient case studies demonstrate that the new model requires significantly fewer time steps than the conventional time-domain models, and is more efficient than the previously established variable-parameter SFA model.