Remote Sensing image super-resolution aims to improve the spectral and/or spatial resolution of the satellite imageries. In order to improve the performance of the CNN-based super-resolution methods, increasing the depth of the network is commonly used. However, this increases computational complexity and training difficulties only with small improvement of the performance. Meanwhile, the CNN kernels treat all the channels equally and cannot take the advantage of the abundant high-frequency information contained in the low-resolution images. To address these problems, Channel attention is one of the mechanisms and has been proven to be useful in many tasks. In this research, we proposed a channel attention-based framework for Remote Sensing Image Super-resolution (CARS) by constructing a novel residual channel attention block (RCAB) to further extract the features. In addition, a densely residual channel attention block (RCAB+) and densely residual spatial attention block (RSAB) were proposed to improve the performance. We adopted a post-upsampling architecture to reduce the computational complexity and time cost. Moreover, transfer learning strategy (CARS+T) was introduced to further improve the SR performance and proved to generate finer edge details. Experimentally, our proposed CARS, CARS_SA and CARS+T achieved competitive quantitative and qualitative results both on Data Fusion Contest Dataset and Pleiades Dataset that we created.