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This paper proposes a new approach for privacy-preserving and verifiable convolutional neural network (CNN) testing, enabling a CNN model developer to convince a user of the truthful CNN performance over non-public data from multiple testers, while respecting model privacy. To balance the security and efficiency issues, three new efforts are done by appropriately integrating homomorphic encryption (HE) and zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) primitives with the CNN testing. First, a CNN model to be tested is strategically partitioned into a private part kept locally by the model developer, and a public part outsourced to an outside server. Then, the private part runs over HE-protected test data sent by a tester and transmits its outputs to the public part for accomplishing subsequent computations of the CNN testing. Second, the correctness of the above CNN testing is enforced by generating zk-SNARK based proofs, with an emphasis on optimizing proving overhead for two-dimensional (2-D) convolution operations, since the operations dominate the performance bottleneck during generating proofs. We specifically present a new quadratic matrix programs (QMPs)-based arithmetic circuit with a single multiplication gate for expressing 2-D convolution operations between multiple filters and inputs in a batch manner. Third, we aggregate multiple proofs with respect to a same CNN model but different testers' test data (i.e., different statements) into one proof, and ensure that the validity of the aggregated proof implies the validity of the original multiple proofs. Lastly, our experimental results demonstrate that our QMPs-based zk-SNARK performs nearly 13.9$\times$faster than the existing QAPs-based zk-SNARK in proving time, and 17.6$\times$faster in Setup time, for high-dimension matrix multiplication.