Spiral bevel gears are widely used in the transmission systems of various industries, such as aviation, aerospace, and automotive industry. Traditional spiral bevel gears are constructed based on the principle of conjugate surfaces. There is relative sliding between the meshing tooth surfaces of the spiral bevel gear, which could lead to a reduction in transmission efficiency. Moreover, misalignment could cause deviation in the contact pattern during the meshing, this affects the meshing performance of bevel gear transmission. Therefore, in this paper, the novel spiral bevel gear based on the principle of curve conjugation is proposed, aiming to achieve zero-sliding contact between meshing tooth surfaces and thereby ensure high transmission efficiency. Furthermore, the influence of misalignment on the meshing performance of this specific bevel gear is studied, mainly focusing on its influence on transmission error. The results show that the proposed bevel gear pair exhibits point contact during the transmission, with the contact point located on the pitch cone. This aligns with the design objective of zero sliding contact. It has been found that the transmission error of the proposed bevel gear is more sensitive to axial deviation and offset distance, and it is the least sensitive to shaft intersection angle. These studies provide new insights into the design of spiral bevel gears and offer the theoretical basis for their practical application.