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In the AC/DC parallel system, AC power system is separated into two areas by the parallel AC line trip. As a result, it is necessary to recover from asynchronous operation. A method to close tripped AC line, "Fast synchronous-reclosing method", is proposed here. This paper consists of two parts: (1) Calculation of the frequency difference limit between the two areas. Energy function is formulated on the condition that fast synchronous-reclosing can be completed satisfactorily. (2) Confirmation of the performance of the fast synchronous-reclosing method in the AC/DC parallel line and frequency control before synchronous-reclosing and damping control of the power swing after reclosing, which were studied using an AC/DC simulator.