A Mixed-mode Computing-in memory (CIM) processor for supporting mixed-precision Deep Neural Network (DNN) processing is proposed. Previous CIM processors cannot exploit energy-efficient computation of mixed-precision DNNs. This paper proposes an energy-efficient mixed-mode CIM processor with two key features: 1) Mixed-Mode Mixed-precision CIM (M3-CIM) which achieves 55.46% energy efficiency improvement. 2) Digital-CIM for In-memory MAC for increasing the throughput of M3-CIM. The proposed CIM processor was simulated in 28nm CMOS technology and occupies 1.96 mm2. It achieves a state-of-the-art energy efficiency of 161.6 TOPS/W with 72.8% accuracy at ImageNet (ResNet50).