Generating high-quality singing voice usually depends on a sizable studio-level singing corpus which is difficult and expensive to collect. In contrast, there is plenty of singing voice data can be found on Internet. However, the found singing data may be mixed by accompaniments or contaminated by environmental noises due to recording conditions. In this paper, we propose a noise robust singing voice synthesizer which incorporates Gaussian Mixture Variational Autoencoder (GMVAE) as the noise encoder to handle different noise conditions, generating clean singing voice from lyrics for target speaker. Specifically, the proposed synthesizer learns a multi-modal latent noise representation of various noise conditions in a continuous space without the use of an auxiliary noise classifier for noise representation learning or clean reference audio during the inference stage. Experiments show that the proposed synthesizer can generate clean and high-quality singing voice for target speaker with MOS close to reconstructed singing voice from ground truth mel-spectrogram with Griffin-Lim vocoder. Experiments also show the robustness of our approach under complex noise conditions.