A new photonic-assisted instantaneous frequency measurement system is presented. It overcomes the latency problem in the reported structures based on the frequency-to-time mapping technique or the frequency-to-power mapping technique that involves a long length of fiber, and at the same time, enables the incoming microwave signal frequency to be measured over a wide frequency range with only small errors. The system generates three low-frequency signals. The phases of the three low-frequency signals are compared. One of the two low-frequency signal phase differences is used to estimate the incoming microwave signal frequency unambiguously over a wide frequency range and the other is used to provide accurate microwave signal frequency measurement. A proof-of-concept experiment is set up. Experimental results show, by measuring the phase difference of two low-frequency signals, the frequency of the input microwave signal can be determined unambiguously in 15 GHz and 500 MHz frequency ranges with errors below ±220 MHz and ±10 MHz respectively. Hence, by using two low-frequency signal phase differences, the input microwave signal frequency can be determined accurately over a wide frequency range. The new photonic-assisted frequency measurement system has a fast response time, which is an order of magnitude shorter than that of the systems based on the frequency-to-time mapping technique and the frequency-to-power mapping technique with a kilometer-long fiber.