Most of the progresses achieved in radar high range resolution profile (HRRP) recognition rely on the closed set condition, where the test sample is from a known class. In realistic scenario, however, the test sample may be drawn from unknown classes, which is regarded as an open set recognition task. In such cases, conventional recognition algorithms will inevitably make a wrong prediction. In this paper, the open set problem is addressed by incorporating the extreme value theory (EVT) into the random forest (RF) classifier. The outputs of RF are analyzed to determine whether the test sample should be rejected as an unknown class. At the training phase, a Weibull-based extreme-value meta-recognition is introduced to describe the statistical characteristics of the known classes. At the testing phase, a probability estimation method is introduced to compute the probabilities of the test sample belonging to known and unknown classes based on trained Weibull distributions. The test sample is assigned to the class of highest probability. Experimental results demonstrate that the proposed method outperforms the state-of-art NN, 1-vs-set machine and W-SVM in rejecting unknown classes.