We propose a neural network for zero-shot voice conversion (VC) without any parallel or transcribed data. Our approach uses pre-trained models for automatic speech recognition (ASR) and speaker embedding, obtained from a speaker verification task. Our model is fully convolutional and non-autoregressive except for a small pre-trained recurrent neural network for speaker encoding. ConVoice can convert speech of any length without compromising quality due to its convolutional architecture. Our model has comparable quality to similar state-of-the-art models while being extremely fast.