We propose a novel heuristic approach, sequential solution method (SSM), for the efficient solution of Continuous Facility Layout Problems (CFLPs). The proposed SSM approach is compared with exact solution methods as well as Genetic Algorithm (GA) and Simulated Annealing (SA) metaheuristic algorithms. We also improved the metaheuristic approaches based on approximating the facility coordinates with the coordinates of the Center of the Smallest Rectangle (CSR) that covers all facilities in the solution. The proposed SSM approach is a recursive heuristic based on the exact solutions of reduced layout problems. Instead of solving the original CFLP with many variables, SSM first generates subproblems (facility clusters) of smaller sizes using a clustering model and then sequentially solves layout subproblems where non-member facilities locations are constrained. Based on an experimental study, we report that the proposed SSM substantially outperforms exact approaches and meta-heuristic approaches and hence provide an alternative approach for efficiently solving large CFLP instances.