We report on the observations of an electron vortex magnetic hole corresponding to a new type of coherent structure in the turbulent magnetosheath plasma using the Magnetospheric Multiscale mission data. The magnetic hole is characterized by a magnetic depression, a density peak, a total electron temperature increase (with a parallel temperature decrease but a perpendicular temperature increase), and strong currents carried by the electrons. The current has a dip in the core region and a peak in the outer region of the magnetic hole. The estimated size of the magnetic hole is about 0.23 rho(i) (similar to 30 rho(e)) in the quasi-circular cross-section perpendicular to its axis, where rho(i) and rho(e) are respectively the proton and electron gyroradius. There are no clear enhancements seen in high-energy electron fluxes. However, there is an enhancement in the perpendicular electron fluxes at 90 degrees pitch angle inside the magnetic hole, implying that the electrons are trapped within it. The variations of the electron velocity components V-em and V-en suggest that an electron vortex is formed by trapping electrons inside the magnetic hole in the cross-section in the M-N plane. These observations demonstrate the existence of a new type of coherent structures behaving as an electron vortex magnetic hole in turbulent space plasmas as predicted by recent kinetic simulations.