A spatial iterative learning control (sILC) method is proposed for a robot to learn a desired path in an unknown environment. When interacting with the environment, the robot initially starts with a predefined trajectory so an interaction force is generated. By assuming that the environment is subjected to fixed spatial constraints, a learning law is proposed to update the robot's reference trajectory so that a desired interaction force is achieved. Different from existing iterative learning control methods in the literature, this method does not require repeating the interaction with the environment in time, which relaxes the assumption of the environment and thus addresses the limits of the existing methods. With the rigorous convergence analysis, simulation and experimental results in two applications of surface exploration and teaching by demonstration illustrate the significance and feasibility of the proposed method.