In this article, we propose a new approach for mobile robot localization and hybrid map building simultaneously without using any odometry hardware system. The proposed method termed as Genetic Bayesian ARAM comprises two main components: (1) steadystate genetic algorithm (SSGA) for self-localization and occupancy grid map building and (2) Bayesian Adaptive Resonance Associative Memory (ARAM) for online topological map building. The model of the explored environment is formed as a hybrid representation, both topological and grid based, and it is incrementally constructed during the exploration process. During occupancy map building, the robot-estimated self-position is updated by SSGA. At the same time, the robot-estimated self-position is transmitted to Bayesian ARAM for topological map building and localization. The effectiveness of our proposed approach is validated by a number of standardized benchmark datasets and real experimental results carried on the mobile robot. Benchmark datasets are used to verify the proposed method capable of generating topological map in different environment conditions. Real robot experiment to verify the proposed method can be implemented in real world.