A programmable logic device including an asynchronous circuit is provided. The programmable logic device includes a lookup table, a first circuit, and a second circuit. The first circuit receives a first signal and a second signal. The second circuit sends a third signal. The first circuit sends a fourth signal and a fifth signal, when receiving the third signal. The fourth signal has the same logic as the first signal. The fifth signal has the same logic as the second signal. The lookup table sends a sixth signal and a seventh signal, when receiving the fourth signal and the fifth signal. The second circuit sends an eighth signal, when receiving the sixth signal and the seventh signal. The first circuit sends a ninth signal, when receiving the eighth signal. The lookup table includes a memory. The sixth signal and the seventh signal are generated from data stored in the memory.