Abstract: To extend the Bézier-stype basis from the traditional polynomial space to other common spaces such as triangular domains,in this paper a basis for trigonometric polynomial space Γ=span1,sint,cost,sin2t,cos2t of order 5 in triangular domain is proposed.The constructed Bézier-type basis in triangular domain have been proved to have the nice properties including positivity,partition of unity,symmetry,boundary representation and linear independence.Its corresponding surfaces of triangular domain can exactly represent spherical patches without rational form.The results of the practical examples shows the representative power of this new basis.