High-precision synchronized measurement data with short measurement latency are required for applications of phasor measurement units (PMUs). This paper proposes a synchrophasor measurement method based on cascaded infinite impulse response (IIR) and dual finite impulse response (FIR) filters, meeting the M-class and P-class requirements in the IEC/IEEE 60255-118-1 standard. A low-group-delay IIR filter is designed to remove out-of-band interference components. Two FIR filters with different center frequencies are designed to filter out the fundamental negative frequency component and obtain synchrophasor estimates. The ratio of the amplitudes of the synchrophasor is used to calculate the frequency according to the one-to-one correspondence between the ratio of the amplitude frequency response of the FIR filters and the frequency. To shorten the response time introduced by IIR filter, a step identification and processing method based on the rate of change of frequency (RoCoF) is proposed and analyzed. The synchrophasor is accurately compensated based on the frequency and the frequency response of the IIR and FIR filters, achieving high-precision synchrophasor and frequency estimates with short measurement latency. Simulation and experiment tests demonstrate that the proposed method is superior to existing methods and can provide synchronized measurement data for M-class PMU applications with short measurement latency.