A scheme is proposed for involving programmable quantum logic gates via teleportation, which is a unique technique in quantum mechanics. In our scheme, considering the inevitable decoherence caused by noisy environment, the quantum states are not maximally entangled. We show the implementation of single qubit quantum gates and controlled-NOT (CNOT) gate, which are universal quantum gates. Hence, any quantum gate can be implemented by using teleportation with non-maximally entangled states. Furthermore, two schemes in differet connections of universal gates are proposed and compared, and our results show the parallel connection outperforms the cascade connection.