Deep convolutional neural networks have achieved remarkable progress in recent years. However, the large volume of intermediate results generated during inference poses a significant challenge to the accelerator design for resource-constraint FPGA. Due to the limited on-chip storage, partial results of intermediate layers are frequently transferred back and forth between on-chip memory and off-chip DRAM, leading to a non-negligible increase in latency and energy consumption. In this paper, we propose block convolution, a hardware-friendly, simple, yet efficient convolution operation that can completely avoid the off-chip transfer of intermediate feature maps at run-time. The fundamental idea of block convolution is to eliminate the dependency of feature map tiles in the spatial dimension when spatial tiling is used, which is realized by splitting a feature map into independent blocks so that convolution can be performed separately on individual blocks. We conduct extensive experiments to demonstrate the efficacy of the proposed block convolution on both the algorithm side and the hardware side. Specifically, we evaluate block convolution on 1) VGG-16, ResNet-18, ResNet-50, and MobileNet-V1 for ImageNet classification task; 2) SSD, FPN for COCO object detection task, and 3) VDSR for Set5 single image super-resolution task. Experimental results demonstrate that comparable or higher accuracy can be achieved with block convolution. We also showcase two CNN accelerators via algorithm/hardware co-design based on block convolution on memory-limited FPGAs, and evaluation shows that both accelerators substantially outperform the baseline without off-chip transfer of intermediate feature maps.