An RF integrated circuit design heavily relies upon experienced experts to iteratively tune the circuit parameters. A Bayesian optimization (BO) method is explored in existing works for automated analog and RF circuit synthesis. The overall performance can be further improved by constructing a model to exploit the correlation among different circuit specifications. In this article, we propose a BO approach for RF circuit synthesis via a multitask neural network enhanced Gaussian process (MTNN-GP). We present a novel multioutput GP model, in which the kernel functions of multiple outputs are constructed from a multitask neural network with shared hidden layers and task-specific layers. Therefore, the correlation between the outputs can be captured by the shared hidden layers. Our proposed MTNN-GP-based BO method is compared with several state-of-the-art BO methods on three real word RF circuits and achieves best performance. The experimental results demonstrate the effectiveness and efficiency of our proposed method.