A preliminary design of a mega-electron-volt (MeV) monochromator with 10−5 energy spread for ultrafast electron diffraction (UED) and ultrafast electron microscopy (UEM) is presented. Such a narrow energy spread is advantageous in both the single shot mode, where the momentum resolution in diffraction is improved, and the accumulation mode, where shot-to-shot energy jitter is reduced. In the single-shot mode, we numerically optimized the monochromator efficiency up to 13% achieving 1.3 million electrons per pulse. In the accumulation mode, to mitigate the efficiency degradation caused by the shot-to-shot energy jitter, an optimized gun phase yields only a mild reduction of the single-shot efficiency, therefore the number of accumulated electrons nearly proportional to the repetition rate. Inspired by the recent work of Qi et al. (Phys Rev Lett 124:134803, 2020), a novel concept of applying reverse bending magnets to adjust the energy-dependent path length difference has been successfully realized in designing a MeV monochromator to achieve the minimum energy-dependent path length difference between cathode and sample. Thanks to the achromat design, the pulse length of the electron bunches and the energy-dependent timing jitter can be greatly reduced to the 10 fs level. The introduction of such a monochromator provides a major step forward, towards constructing a UEM with sub-nm resolution and a UED with ten-femtosecond temporal resolution. The one-to-one mapping between the electron beam parameter and the diffraction peak broadening enables a real-time nondestructive diagnosis of the beam energy spread and divergence. The tunable electric–magnetic monochromator allows the scanning of the electron beam energy with a 10−5 precision, enabling online energy matching for the UEM, on-momentum flux maximizing for the UED and real-time energy measuring for energy-loss spectroscopy. A combination of the monochromator and a downstream chicane enables “two-color” double pulses with femtosecond duration and the tunable delay in the range of 10 to 160 fs, which can potentially provide an unprecedented femtosecond time resolution for time resolved UED.