Blind modulation classification is widely used in various military and civilian applications. Characterized by its exemption from likelihood calculation and the ability of using well-trained models, feature-based (FB) classifiers are popular with their high computational efficiency. In recent years, Deep Neural Networks based methods have shown significant improvement in the classification accuracy. However, the performance of FB methods decreases rapidly under low signal-to-noise ratios. To overcome this shortcoming, this letter proposes a joint denoising and modulation classification method based on Multitask Learning, where a denoising network and a classification network are simultaneoulsy trained in an end-to-end manner. In addition, the focal loss function is adopted to highlight the importance of hard-to-classify samples during training. Our numerical experiments show that the proposed method can effectively improve the classification accuracy, and outperform state-of-the-art methods. For example, under the 0dB SNR condition, the performance of our proposed Multitask CNN method is 20% higher than that of the traditional CNN method.