This paper proposes a novel general variable neighborhood search (GVNS) algorithm to solve the no-idle flowshop scheduling problem with the makespan criterion. The initial solution of the GVNS is generated using the FRB5 heuristic. In the outer loop, insert and swap operations are employed to shake the permutation. In the inner loop of variable neighborhood descent procedure, two effective algorithms, namely, Iterated Greedy (IG) and Variable Block Insertion Heuristic (VBIH) algorithms are used. Note that, an effective referenced insertion scheme is employed in these IG and VBIH algorithms. The proposed GVNS algorithm is compared with the standard IG algorithm using the benchmark instances. The computational experiments show that the GVNS performs much better than the standard IG. Furthermore, the results of the standard IG and GVNS algorithms are compared with the current best-known solutions reported in the literature. The computational results show that the proposed GVNS algorithm improves some of the current best-known solutions in the literature. Consequently, it can be said that the GVNS is very effective for the no-idle flowshop scheduling problem with the makespan criterion.