Rydberg atoms are atoms in highly excited states with large principal quantum numbers n, and long lifetimes. The large Rydberg atom polarizability and strong dipole transitions between energetically nearby states are highly sensitive to electric fields. The new developed scheme for microwave electric field precision measurement is based on quantum interference effects (electromagnetically induced transparency and Autler-Townes splitting) in Rydberg atoms contained in a dielectric vapor cell. The minimum measured strengths of microwave electric fields of the new scheme are far below the standard values obtained by traditional antenna methods. And it has several advantages, such as self-calibration, non-perturbation to the measured field, a broadband measurement frequency range and so on, is next-generation electric field standard. In this review, we describe work on the new method for measuring microwave electric field based on Rydberg atoms. We introduce the basic theory and experimental techniques of the new method, and discuss the future development direction.