EPR state as the most basic quantum entangled state plays an important role in quantum teleportation. In this work, the universal single-qubit quantum teleportation adapted to any type of EPR channel is studied and generalized to universal N-qubit quantum teleportation. In the single-bit quantum teleportation mode with four kinds of EPR states as quantum channels respectively, design single-bit universal circuits by analyzing the relationship between the EPR and the quantum gate, then design a two-bit standard quantum teleportation circuit and use Mathematica to verify the correctness of the circuit, and then generalize it to an N-bit quantum teleportation circuit, the next step, the single-qubit universal circuit and the N-qubit quantum teleportation circuit are implemented for fusion, finally any N-bit quantum teleportation universal circuit is designed. The universal circuits for N-particle quantum bits perform unitary transformation with parameters by the recipient of the information, where the parameters are determined by the type of EPR prepared, which solves the problem of information transmission failure due to an error in the EPR preparation center.