In this paper, the permutation flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs is considered, and a simulated annealing algorithm (SA) and two modified SAs (MSA1 and MSA2) are proposed. In the first phase, the proposed algorithms are used to minimise CTV of jobs without any right shifting of completion times of jobs on the last machine (RSCT). As followed in the literature some times, the RSCT (except that of the last job) is attempted in the second phase, and in the third phase, we convert sequences so as to follow the V-shaped property with respect to processing time of jobs on the last machine, followed by RSCT except that of the last job, so that the makespan and the machine utilisation in the shop floor remain the same. We present an extensive computational evaluation of the existing and the proposed heuristic algorithms. © The Author(s) 2019.