Secure Machine Learning as a Service (MLaaS) is a viable solution where clients seek secure ML computation delegation while protecting sensitive data. We propose an efficient method to securely evaluate deep standard convolutional neural networks based on residue number system variant of Cheon-Kim-Kim-Song (RNS-CKKS) scheme in the manner of batch inference. In particular, we introduce a packing method calledChannel-By-Channel Packingthat maximizes the slot compactness and Single-Instruction-Multiple-Data (SIMD) capabilities in ciphertexts. We also propose a new method for homomorphic convolution evaluation calledChannel-By-Channel Convolution, which minimizes the additional heavy operations during convolution layers. Simulation results show that our work has improvements in amortized runtime for inference, with a factor of 5.04 and 5.20 for ResNet-20 and ResNet-110, respectively, compared to the previous results. We note that our results almost simulate the original backbone models, with classification accuracy differing from the backbone within 0.02%p. Furthermore, we show that the client's rotation key size generated and transmitted can be reduced from 105.6 GB to 6.91 GB for ResNet models during an MLaaS scenario. Finally, we show that our method can be combined with previous methods, providing flexibility for selecting batch sizes for inference.