Humans can balance very well during walking, even when perturbed. But it seems difficult to achieve robust walking for bipedal robots. Here we describe the simplest balance controller that leads to robust walking for a linear inverted pendulum (LIP) model. The main idea is to use a linear function of the body velocity to determine the next foot placement, which we call linear foot placement control (LFPC). By using the Poincaré map, a balance criterion is derived, which shows that LFPC is stable when the velocity-feedback coefficient is located in a certain range. And that range is much bigger when stepping faster, which indicates "faster stepping, easier to balance". We show that various gaits can be generated by adjusting the controller parameters in LFPC. Particularly, a dead-beat controller is discovered that can lead to steady-state walking in just one step. The effectiveness of LFPC is verified through Matlab simulation as well as V-REP simulation for both 2D and 3D walking. The main feature of LFPC is its simplicity and inherent robustness, which may help us understand the essence of how to maintain balance in dynamic walking.