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In their most aggressive form, the mortality rate of gliomas is high. Accurate segmentation is important for surgery and treatment planning, as well as for follow-up evaluation. In this paper, we propose to segment brain tumors using a Deep Convolutional Neural Network. Neural Networks are known to suffer from overfitting. To address it, we use Dropout, Leaky Rectifier Linear Units and small convolutional kernels. To segment the High Grade Gliomas and Low Grade Gliomas we trained two different architectures, one for each grade. Using the proposed method it was possible to obtain promising results in the 2015 Multimodal Brain Tumor Segmentation (BraTS) data set, as well as the second position in the on-site challenge.