Oblivious inference enables the cloud to provide neural network inference-as-a-service (NN-IaaS), whilst neither disclosing the client data nor revealing the servers model. However, the privacy guarantee under oblivious inference usually comes with a heavy cost of efficiency and accuracy. We propose Popcorn, a concise oblivious inference framework entirely built on the Paillier homomorphic encryption scheme. We design a suite of novel protocols to compute non-linear activation and max-pooling layers. We leverage neural network compression techniques (i.e., neural weights pruning and quantization) to accelerate the inference computation. To implement the Popcorn framework, we only need to replace algebraic operations of existing networks with their corresponding Paillier homomorphic operations, which is extremely friendly for engineering development. We first conduct the performance evaluation and comparison based on the MNIST and CIFAR-10 classification tasks. Compared with existing solutions, Popcorn brings a significant communication overhead deduction, with a moderate runtime increase. Then, we benchmark the performance of oblivious inference on ImageNet. To our best knowledge, this is the first report based on a commercial-level dataset, taking a step towards the deployment to production.