The Space-Free Multi-Row Facility Layout problem (SF-MRFLP) seeks for a non-overlapping layout of departments (facilities) on a given number of rows satisfying the following constraints: no space is allowed between two adjacent facilities and the left-most department of the arrangement must have zero abscissa. The objective is to minimize the total communication cost among facilities. In this paper, a Variable Neighborhood Search (VNS) algorithm is proposed to solve this -Hard problem. It has practical applications in the context of the arrangement of rooms in buildings, semiconductor wafer fabrication, or flexible manufacturing systems. A thorough set of preliminary experiments is conducted to evaluate the influence of the proposed strategies and to tune the corresponding search parameters. The best variant of our algorithm is tested over a large set of 528 instances previously used in the related literature. Experimental results show that the proposed algorithm improves the state-of-the-art methods, reaching all the optimal values or, alternatively, the best-known values (if the optimum is unknown) but in considerably shorter computing times. These results are further confirmed by conducting a Bayesian statistical analysis.