This paper extends a monotonically convergent algorithm for quantum optimal control to treat systems with dissipation. The algorithm working with the density matrix is proved to exhibit quadratic and monotonic convergence. Several numerical tests are implemented in three-level model systems. The algorithm is exploited to control various targets, including the expectation value of a Hermitian operator, the modulus square of the expectation value of a non-Hermitian operator, and off-diagonal elements of the density matrix.