Glioblastoma (GBM) is the most common and deadly malignant brain tumor. For personalized treatment, an accurate pre-operative prognosis for GBM patients is highly desired. Recently, many machine learning-based methods have been adopted to predict overall survival (OS) time based on the pre-operative mono- or multi-modal imaging phenotype. The genotypic information of GBM has been proven to be strongly indicative of the prognosis; however, this has not been considered in the existing imaging-based OS prediction methods. The main reason is that the tumor genotype is unavailable pre-operatively unless deriving from craniotomy. In this paper, we propose a new deep learning-based OS prediction method for GBM patients, which can derive tumor genotype-related features from pre-operative multimodal magnetic resonance imaging (MRI) brain data and feed them to OS prediction. Specifically, we propose a multi-task convolutional neural network (CNN) to accomplish both tumor genotype and OS prediction tasks jointly. As the network can benefit from learning tumor genotype-related features for genotype prediction, the accuracy of predicting OS time can be prominently improved. In the experiments, multimodal MRI brain dataset of 120 GBM patients, with as many as four different genotypic/molecular biomarkers, are used to evaluate our method. Our method achieves the highest OS prediction accuracy compared to other state-of-the-art methods.