Social intelligence is an important requirement for enabling robots to collaborate with people. In particular, human path prediction is an essential capability for robots in that it prevents potential collision with a human and allows the robot to safely make larger movements. In this paper, we present a method for predicting the trajectory of a human who follows a haptic robotic guide without using sight, which is valuable for assistive robots that aid the visually impaired. We apply a deep learning method based on recurrent neural networks using multimodal data: (1) human trajectory, (2) movement of the robotic guide, (3) haptic input data measured from the physical interaction between the human and the robot, (4) human depth data. We collected actual human trajectory and multimodal response data through indoor experiments. Our model outperformed the baseline result while using only the robot data with the observed human trajectory, and it shows even better results when using additional haptic and depth data.