This paper addresses finite-time projective synchronization of stochastic complex-valued neural networks (SCVNNs) with probabilistic time-varying delays (PTVs). First, in the complex domain, PTVs are introduced into the studied model and a novel feedback control scheme is constructed. Next, based on inequalities techniques and the Lyapunov stability approach, some novel projective synchronization criteria are established by decomposing SCVNNs into two equivalent real-valued systems. Moreover, a setting time function is created by employing lemma 4. Compared with previous researches, our theory content is an extension and complement to known results. Finally, numerical simulation is presented to validate the effectiveness of theoretical analysis results.