A vehicle collision avoidance apparatus and method are provided. The method includes identifying, by a controller, whether an obstacle is a vehicle or a pedestrian and collecting information required for calculating a minimum braking time and a minimum steering time. The controller is configured to calculate the minimum braking time to avoid a collision with the obstacle and the minimum steering time to avoid a collision with an obstacle. In addition, the a controller is configured to sequentially operating braking and steering of a traveling vehicle based on the minimum steering time depending on a type of identified obstacle.