The significant challenge for steady-state process optimization using rigorous models is the intractable convergence of complex flowsheet in equation-oriented (EO) modeling environments, which could be resolved to a large extent through using the time-relaxation algorithm based on pseudo-transient continuation (PTC) models. However, such approach often leads to computational inefficiency due to large computational burden from dynamic simulation. In this paper, we develop a fast-tailed algorithm using PTC models, which combines dynamic and steady-state simulation instead of using dynamic simulation alone. To further improve the efficiency of dynamic simulation, a tolerances-relaxation integration strategy is proposed. Several examples from the literature are used to illustrate the capability of the proposed algorithm. The computational results demonstrate that the proposed algorithm is faster than the time-relaxation algorithm. In addition, the proposed algorithm is much easier to be implemented in various EO environments as it is compatible to the inherent optimization solvers in these environments.