University course timetabling problem (UCTP) is a NP hard problem and cannot be solved using some universal principles. The intricate relationship between subjects, timeslots and classes makes its complicated to obtain optimal solution. Thus, to obtain optimal solution of timetabling problem is a challenging task. In this study hybrid Mountain Gazelle Particle Swarm Optimization (MGPSO) and Hybrid Mountain Gazelle Genetic Optimization Algorithm (HMGGOA) is used to resolve timetabling difficulty and their results are compared with Hybrid PSO with Constraint Based Reasoning (PSO-CBR), Hybrid PSO with local Search (PSO-LS) and Hybrid Genetic Algorithm with Constraint Based Reasoning (GA-CBR). Each algorithm run five times and their run time values and fitness function values are stored to compare the performance of proposed algorithm (MGPSO, HMGGOA). After compare the presentation it is observed that HMGGOA gives best value in minimum time. So, HMGGOA perform good as compared to other algorithms (MGPSO, PSO-CBR, GA-CBR, PSO-LS).