We investigate barrier tunneling of quasiparticles in double-Weyl semimetals. Being the anisotropic dispersion, it exhibits different scattering properties for different barrier orientations. We discuss two cases. In the first case where the barrier is perpendicular to linear momentum direction, we show that the incoming quasiparticles can fully pass through the barrier at normal incidence. This is known as Klein tunneling, a familiar phenomenon in the Graphene. The full transmission also occurs for some other special angles determined by the resonance condition between the barrier width and the wave vector in the barrier. In the second case where the barrier is perpendicular to quadratic momentum direction, the incoming quasiparticles can be fully reflected by the barrier at normal incidence, which is known as anti-Klein tunneling. As the energy of incident quasiparticles changes, it induces a transition from Klein tunneling to anti-Klein tunneling. When the band gap is opened, it has impact on the chirality and Berry phase. So the transmission coefficient is also changed.
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