Analysis: The analytical expression of parabola is called vertex, and the vertex coordinates are written directly according to the characteristics of vertex.

Solution: Solution: Because y=(x-3)2+ 1 is the vertex of a parabola,

According to the coordinate characteristics of vertices, the vertex coordinate of is (3, 1).

So choose B.

Comments: This question examines the nature of quadratic function. The quadratic function is y=a(x-h)2+k and the vertex coordinate is (h, k).