To construct a tight frame for a given vector, joint quantum measurement of teleportation was investigated, and a construction method of tight frame was proposed. The generalized construction method of tight frame is based on joint quantum measurement. Firstly, arrange the given vector into a coefficient matrix, then obtain its left unitary, right unitary and singular value matrix by singular value decomposition. Secondly, find a base including a column whose coefficient matrix is just the non-zero part of the singular value matrix. At the end, arrage the rest colomns of the base into non-zero part of the singular value matrix, then get the rest tight frame columns by singular value reconstruction.