In this letter, we first present a rank-revealing matrix factorization algorithm by using randomization called randomized truncated pivoted QLP (RTp-QLP) to approximate an input matrix. For a dense and large n₁ × n₂ matrix with numerical rank k, RTp-QLP needs only a few passes over the matrix (regardless of k) and O(n₁n₂d) floating-point operations, where d is much smaller than both n₁ and n₂. Next, we develop a robust principal component analysis (RPCA) method by utilizing RTp-QLP. In addition, we propose a rank estimation technique that efficiently solves the RPCA task. RTp-QLP is highly accurate and numerically stable. Our proposed RTp-QLP-based RPCA method yields the optimal solution, and it is faster than existing methods. Our simulation results support our claims.