Deep convolutional neural networks (CNNs) are computationally and memory intensive. In CNNs, intensive multiplication can have resource implications that may challenge the ability for effective deployment of inference on resource-constrained edge devices. This paper proposes GhostShiftAddNet, where the motivation is to implement a hardware-efficient deep network: a multiplication-free CNN with fewer redundant features. We introduce a new bottleneck block, GhostSA, that converts all multiplications in the block to cheap operations. The bottleneck uses an appropriate number of bit-shift filters to process intrinsic feature maps, then applies a series of transformations that consist of bit-wise shifts with addition operations to generate more feature maps that fully learn to capture information underlying intrinsic features. We schedule the number of bit-shift and addition operations for different hardware platforms. We conduct extensive experiments and ablation studies with desktop and embedded (Jetson Nano) devices for implementation and measurements. We demonstrate the proposed GhostSA block can replace bottleneck blocks in the backbone of state-of-the-art networks architectures and gives improved performance on image classification benchmarks. Further, our GhostShiftAddNet can achieve higher classification accuracy with fewer FLOPs and parameters (reduced by up to 3x) than GhostNet. When compared to GhostNet, inference latency on the Jetson Nano is improved by 1.3x and 2x on the GPU and CPU respectively. Code is available open-source on \url{https://github.com/JIABI/GhostShiftAddNet}.