A pet door with locking flaps, or lockable pet door. The lockable pet door includes a barrier flap surrounded by one or more locking flaps mounted in the pet door frame. The locking flaps, the barrier flap, and the pet door frame cooperate to provide selective direction control allowing ingress, egress, both, or neither. Each locking flap is independently and selectively attached to the frame of the pet door to prevent movement of the locking flap. Each locking flap defines a through opening. In use, the animal passes through the locking flap on the entry side of the pet door and the locking flap on the exit side moves with the barrier flap. When locked, each locking flap prevents the barrier flap from pivoting to that side of the pet door blocking passage in that direction.