In this paper, we proposed a biased support vector machine (Biased-SVM) with self-constructed Universum (termed as U-BSVM) to solve the PU learning problem. We first treat the PU problem as an imbalanced binary classification problem by labeling all the unlabeled inputs as negative with noise, then inspired by the Universum-SVM (U-SVM), introduce the Universum data set which is constructed from the original dataset to improve the performance of Biased-SVM. We intent to use the constructed Universum data set to catch some prior information of the ground-truth decision boundary. Obviously, different Universum data set leads to different result, so several methods to construct the appropriate Uninversum data set are also compared and suggested. Experiment results show the efficiency of our method for PU learning problem.