In order to flexibly control the shape of the bi-cubic Coons patch and improve the bicubic Coons patch, we construct a triangular mixing function group consisting of four functions with shape parameter λ, named TC-Hermite basis. The TC-Hermite basis has properties of endpoints, monotonicity of parameter λ, adjustability of shape etc.. Based on the TC-Hermite basis, we also construct a new Coons patch with shape parameters, called TC-Coons patch. The TC-Coons patch not only adjusts its shape through shape parameters, but also accurately represents quadratic surfaces, such as sphere and torus. Furthermore, the application of the TC-Coons patch in geometric modeling is also discussed.