Identifying terrain type is important for safely operating robots exploration in unstructured environments. In this letter, we firstly proposed a novel tapered whisker-based semi-supervised reservoir computing (TWSSRC) system for improving terrain classification and terrain property estimation for traversability assessment with low computing cost. Three Hall sensors are used to capture the vibration at different locations of the tapered whisker. It could provide morphological computation power to achieve frequency separation in the time domain simultaneously without any data procession and only with the help of an additional simple linear regression, different signals can be classified. The movement of the robot on different types of terrain will result in different vibration behaviors of the whiskers and the whiskered robot can learn from prior physical experiences through cost-efficient self-supervised reservoir computing to achieve auto-labeling of new terrain and terrain classification. Experimental results demonstrate that this method can achieve good performance when the robot encounters new terrain and can accurately estimate the property of the unknown terrain surface at different robot speeds.