<p>Secret sharing has become a important cryptographic primitive and been widely used. And quantum secret sharing is a quantum approach to achieve secret sharing. The (<i>t</i>,&#xa0;<i>n</i>) threshold quantum secret sharing requires only t participants out of n to cooperate to recover the secret, which is more flexible than the (<i>n</i>,&#xa0;<i>n</i>) scheme. However, most (<i>t</i>,&#xa0;<i>n</i>) threshold schemes basically involve quantum entanglement, and the preparation of entangled states as well as entanglement swapping are relatively complex. In this paper, we propose a (<i>t</i>,&#xa0;<i>n</i>) threshold quantum secret sharing scheme with authentication by using the Lagrange interpolation polynomial based on single photons. Unlike other (<i>t</i>,&#xa0;<i>n</i>) threshold schemes, it does not involve entangled states or entanglement swapping. And the distributor authenticate the participants without revealing the full identity key. In addition, secret sharing is based on Lagrange interpolation polynomial implementation, allowing any t participants to recover the secret. Analysis shows that the scheme can resist external eavesdroppers and dishonest participants. Compared with other schemes, this scheme has the following advantages: (1) it is easy to implement; (2) the (<i>t</i>,&#xa0;<i>n</i>) threshold scheme increases the flexibility of the scheme; (3) the identity key can be reused. </p>