  In this paper we present an exact solution of Einstein's field equations
describing the Schwarzschild black hole in dark energy background. It is also
regarded as an embedded solution that the Schwarzschild black hole is embedded
into the dark energy space producing Schwarzschild-dark energy black hole. It
is found that the space-time geometry of Schwarzschild-dark energy solution is
non-vacuum Petrov type $D$ in the classification of space-times. We study the
energy conditions (like weak, strong and dominant conditions) for the
energy-momentum tensor of the Schwarzschild-dark energy solution. We also find
that the energy-momentum tensor of the Schwarzschild-dark energy solution
violates the strong energy condition due to the negative pressure leading to a
repulsive gravitational force of the matter field in the space-time. It is
shown that the time-like vector field for an observer in the Schwarzschild-dark
energy space is expanding, accelerating, shearing and non-rotating. We
investigate the surface gravity and the area of the horizons for the
Schwarzschild-dark energy black hole.
