Summary: Chameleon swarm algorithm (CSA) is a newly proposed swarm intelligence algorithm inspired by the chameleon’s foraging strategies of tracking, searching and attacking targets, and has shown well competitive performance with other state-of-the-art algorithms. Interestingly, CSA mathematically models and implements the steps of chameleon’s unique food-seeking behavior. Nevertheless, the original CSA suffers from the challenges of insufficient exploitation ability, ease of falling into local optima, and low convergence accuracy in complex large-scale applications. Aiming at these challenges, an efficient enhanced chameleon swarm algorithm termed MCSA, combined with fractional-order calculus, sinusoidal adjustment of parameters and crossover-based comprehensive learning (CCL) strategy, is developed in this paper. Firstly, a good fractional-order calculus strategy is added to update the chameleon’s attack velocity, which heightens the local search ability of CSA and accelerates the convergence speed of the algorithm; meanwhile, the sinusoidal adjustment of parameters is adopted to provide a better balance between exploration and exploitation of CSA. Secondly, the CCL strategy is used for the mutation to increase the diversity of the population and avoid becoming trapped in local optima. Three strategies enhance the overall performance and efficiency of the native CSA. Finally, the superiority of the presented MCSA is verified in detail by comparing it with native CSA and several state-of-the-art algorithms on the well-known 23 benchmark test functions, CEC2017 and CEC2019 test suites, respectively. Furthermore, the practicability of MCSA is also highlighted by six real-world engineering designs and two truss topology optimization problems. Simulation results demonstrate that MCSA has strong competitive capabilities and promising prospects. MCSA is potentially an excellent meta-heuristic algorithm for solving engineering optimization problems.