Recently, a new swarm intelligence optimization algorithm called the remora optimization algorithm (ROA) was proposed. ROA simulates the remora’s behavior of the adsorption host and uses some formulas of the sailfish optimization (SFO) algorithm and whale optimization algorithm (WOA) to update the solutions. However, the performance of ROA is still unsatisfactory. When solving complex problems, ROA’s convergence ability requires further improvement. Moreover, it is easy to fall into local optimization. Since the remora depends on the host to obtain food and optimize ROA performance, this paper introduces the mutualistic strategy to strengthen the symbiotic relationship between the remora and the host. Meanwhile, chaotic tent mapping and roulette wheel selection are added to further improve the algorithm’s performance. By incorporating the above improvements, this paper proposes an improved remora optimization algorithm with a mutualistic strategy (IROA) and uses 23 benchmark functions in different dimensions and CEC2020 functions to validate the performance of the proposed IROA. Experimental studies on six classical engineering problems demonstrate that the proposed IROA has excellent advantages in solving practical optimization problems.