Automatic singing evaluation independent of reference melody is a challenging task due to its subjective and multi-dimensional nature. As an essential attribute of singing voices, vocal timbre has a non-negligible effect and influence on human perception of singing quality. However, no research has been done to include timbre information explicitly in singing evaluation models. In this paper, a data-driven model TG-Critic is proposed to introduce timbre embeddings as one of the model inputs to guide the evaluation of singing quality. The trunk structure of TG-Critic is designed as a multi-scale network to summarize the contextual information from constant-Q transform features in a high-resolution way. Furthermore, an automatic annotation method is designed to construct a large three-class singing evaluation dataset with low human-effort. The experimental results show that the proposed model outperforms the existing state-of-the-art models in most cases.