  Superconducting diode effect (SDE) with nonreciprocal supercurrent transport
has attracted intense attention recently, not only for its intriguing physics,
but also for its great application potential in superconducting circuits. It is
revealed in this work that planar Josephson junctions (JJs) based on type-II
Weyl semimetal (WSM) MoTe$_2$ can exhibit a prominent SDE due to the emergence
of asymmetric Josephson effect (AJE) in perpendicular magnetic fields. The AJE
manifests itself in a very large asymmetry in the critical supercurrents with
respect to the current direction. The sign of this asymmetry can also be
effectively modulated by the external magnetic field. Considering the special
noncentrosymmetric crystal symmetry of MoTe$_2$, this AJE is understood in
terms of the Edelstein effect, which induces a nontrivial phase shift in the
current phase relation of the junctions. Besides these, it is further
demonstrated that the rectification of supercurrent in such MoTe$_2$ JJs with
the rectification efficiency up to 50.4%, unveiling the great application
potential of WSMs in superconducting electronics.
