One of the reasons why it is difficult for the brain to perform backpropagation (BP) is the weight transport problem, which argues forward and feedback neurons cannot share the same synaptic weights during learning in biological neural networks. Recently proposed algorithms address the weight transport problem while providing good performance similar to BP in large-scale networks. However, they require bidirectional connections between the forward and feedback neurons to train their weights, which is observed to be rare in the biological brain. In this work, we propose an Activation Sharing algorithm that removes the need for bidirectional connections between the two types of neurons. In this algorithm, hidden layer outputs (activations) are shared across multiple layers during weight updates. By applying this learning rule to both forward and feedback networks, we solve the weight transport problem without the constraint of bidirectional connections, also achieving good performance even on deep convolutional neural networks for various datasets. In addition, our algorithm could significantly reduce memory access overhead when implemented in hardware.