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Generative adversarial network (GAN) has become one of the most important neural network models for classical unsupervised machine learning. A variety of discriminator loss functions have been developed to train GAN's discriminators and they all have a common structure: a sum of real and fake losses that only depends on the actual and generated data respectively. One challenge associated with an equally weighted sum of two losses is that the training may benefit one loss but harm the other, which we show causes instability and mode collapse. In this paper, we introduce a new family of discriminator loss functions that adopts a weighted sum of real and fake parts, which we call adaptive weighted loss functions or aw-loss functions. Using the gradients of the real and fake parts of the loss, we can adaptively choose weights to train a discriminator in the direction that benefits the GAN's stability. Our method can be potentially applied to any discriminator model with a loss that is a sum of the real and fake parts. Experiments validated the effectiveness of our loss functions on an unconditional image generation task, improving the baseline results by a significant margin on CIFAR-10, STL-10, and CIFAR-100 datasets in Inception Scores and FID.