In this work, the flowshop scheduling problem is considered with the objective of minimising the completion-time variance (CTV) of jobs, and an Ant Colony Optimisation (ACO) algorithm is presented. Two implementations of the Modified Ant Colony Optimisation algorithm (MACO-I and MACO-II) are proposed to solve the permutation flowshop scheduling problem. The proposed ant-colony-algorithm implementations have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed MACO implementations are compared with various algorithms and with the best CTV of jobs reported in the literature. The proposed MACO implementations are found to perform very well in minimising the chosen performance measure. © 2012 Copyright Taylor and Francis Group, LLC.