Segmenting medical images accurately and reliably is important for disease diagnosis and treatment. It is a challenging task because of the wide variety of objects' sizes, shapes, and scanning modalities. Recently, many convolutional neural networks (CNN) have been designed for segmentation tasks and achieved great success. Few studies, however, have fully considered the sizes of objects, and thus most demonstrate poor performance for small objects segmentation. This can have a significant impact on the early detection of diseases. This paper proposes a Context Axial Reserve Attention Network (CaraNet) to improve the segmentation performance on small objects compared with several recent state-of-the-art models. We test our CaraNet on brain tumor (BraTS 2018) and polyp (Kvasir-SEG, CVC-ColonDB, CVC-ClinicDB, CVC-300, and ETIS-LaribPolypDB) segmentation datasets. Our CaraNet achieves the top-rank mean Dice segmentation accuracy, and results show a distinct advantage of CaraNet in the segmentation of small medical objects.