Burst image super-resolution is an ill-posed problem that aims to restore a high-resolution (HR) image from a se- quence of low-resolution (LR) burst images. To restore a photo-realistic HR image using their abundant information, it is essential to align each burst of frames containing ran- dom hand-held motion. Some kernel prediction networks (KPNs) that are operated without external motion compen- sation such as optical flow estimation have been applied to burst image processing as implicit image alignment mod- ules. However, the existing methods do not consider the interdependencies among the kernels of different sizes that have a significant effect on each pixel. In this paper, we propose a novel weighted multi-kernel prediction network (WMKPN) that can learn the discriminative features on each pixel for burst image super-resolution. Our experi- mental results demonstrate that WMKPN improves the vi- sual quality of super-resolved images. To the best of our knowledge, it outperforms the state-of-the-art within ker- nel prediction methods and multiple frame super-resolution (MFSR) on both the Zurich RAW to RGB and BurstSR datasets.