In order to elucidate the neural mechanisms involved in the perception of the three-dimensional (3D) orientation of a surface, we trained monkeys to discriminate the 3D orientation of a surface from binocular disparity cues using a Go/No-go type delayed-matching-to-sample (DMTS) task and examined the properties of the surface-orientation-selective (SOS) neurons. We recorded 57 SOS neurons from the caudal part of the lateral bank of the intraparietal sulcus (area CIP) of three hemispheres of two Japanese monkeys (Macaca fuscata). We tested 29 of 57 SOS neurons using the square plate of a solid figure stereogram (SFS) and random-dot stereogram (RDS) without perspective cues; almost all of the tested neurons (28/29) showed surface orientation selectivity for the SFS and/or the RDS without perspective cues. Eight of these 28 neurons (28.6%) showed selectivity for both the RDS and SFS, 7 (25.0%) were dominantly selective for the RDS, and 13 (46.4%) were dominantly selective for the SFS. These results suggest that neurons that show surface orientation tuning for the RDS without perspective cues compute surface orientation from the gradient of the binocular disparity given by the random-dot across the surface. On the other hand, neurons that show surface orientation tuning for the SFS without perspective cues may represent surface orientation primarily from the gradient of the binocular disparity along the contours. In conclusion, the SOS neurons in the area CIP are likely to operate higher order processing of disparity signals for surface perception by integrating the input signals from many disparity-sensitive neurons with different disparity tuning.