According　to　the　theory　of　circuit，the　admittance　of　the　fractional　order　RLα-Cβ parallel circuit　is obtained　in　the　condition　α=β and　CR2/L<<1，a　simple　expression　of　the　phase-frequency characteristic of　the　parallel　resonant　circuit　is　deduced，and　the　analysis　and　discussion　are　carried　out.The theoretical　analysis　is　in　agreement　with　simulation　result，and　thus　the　law　of　phase-frequency　characteristic with　the　change　of　element　parameters　and　fractional　order　is　found.