For Near-zero-energy buildings, the application of building insulation materials is widely used. Anchor bolts, as a fixing element of insulators, have been applied to increase the safety of insulators; however, due to their high thermal conductivity they can cause point thermal bridges and lead to a negative effect on the insulation function of building envelopes. Very few studies, though, have systematically explored the issuer. This study therefore proposes a prediction approach, with a 3D model developed by MATLAB, to investigate the effect of anchors on thermal performance of building envelopes with insulation layers fixed by anchors. It also provides a new indicator, namely the equivalent effective thermal conductivity of insulators which can be used in many popular building energy prediction packages. Simulation results reveal a complicated thermal impact of anchor bolts on an external building envelope, which would be affected by many parameters of different envelope contents. For example, for glass fiber insulation materials with aluminum alloy anchor bolts, the effective thermal conductivity would rise by up to 18 times, and the corresponding envelope thermal transmittance would increase by 33%. This novel model can provide an accurate and easy method to evaluate the thermal effect of anchor bolts, and it is applicable to anchors made of any material. The proposed method could be a reference in energy performance prediction for high-performance buildings.