This paper is about formulating the agnostic matrix phase retrieval (AMPR) as a rank-restricted largest eigenvalue problem by applying the second-order Stein’s identity and propose a new spectrum truncation power iteration (STPower) method to obtain the desired low-rank matrix efficiently. Also, we show a favorable rank recovery result by adopting the STPower method, i.e., a near-optimal statistical convergence rate under some relatively general model assumptions from a wide range of applications. Extensive simulations verify our theoretical analysis and showcase the strength of STPower compared with the other existing counterparts.