Protein tertiary structure prediction is an important open challenge in bioinformatics and requires effective methods to accurately evaluate the quality of protein 3-D models generated computationally. Many quality assessment (QA) methods have been proposed over the past three decades. However, the accuracy or robustness is unsatisfactory for practical applications. In this paper, two new heuristic QA methods are proposed: MUfoldQA_S and MUfoldQA_C. The MUfoldQA_S is a quasi-single-model QA method that assesses the model quality based on the known protein structures with similar sequences. This algorithm can be directly applied to protein fragments without the necessity of building a full structural model. A BLOSUM-based heuristic is also introduced to help differentiate accurate templates from poor ones. In MUfoldQA_C, the ideas from MUfoldQA_S were combined with the consensus approach to create a multi-model QA method that could also utilize information from existing reference models and have demonstrated improved performance. Extensive experimental results of these two methods have shown significant improvement over existing methods. In addition, both methods have been blindly tested in the CASP12 world-wide competition in the protein structure prediction field and ranked as top performers in their respective categories.