We present BioBug, a bionic cognitive response navigation algorithm for mobile robots based on neuroethology principles. It includes a biological antenna model for environment perception and an improved Bug algorithm for motion planning and control. The biological antenna model delineates the interested sensing areas, and thus decreases the computational burden. Then, this obtained environment stimulation is responded to generate the corresponding walking behavior according to BioBug. Simulations and experiments have been carried out in different conditions of obstacle density and boundary shape through algorithm comparisons. Compared with the competitors, BioBug is characterized by not only a smaller path length, but also shorter time for obstacle escape. The results demonstrate the practicality, environment robustness, and obstacle avoidance efficiency of the algorithm.