  We devise a lucid and straightforward way for explicitly constructing
quasi-periodic wave solutions (also called multi-periodic wave solutions) of
supersymmetric equations in superspace $\mathbb{R}_\Lambda^{2,1}$ over
two-dimensional Grassmann algebra $G_1(\sigma)$. Once a nonlinear equation is
written in a bilinear form, its quasi-periodic wave solutions can be directly
obtained by using a formula. Moreover, properties of these solutions are
investigated in detail by analyzing their structures, plots and asymptotic
behaviors. The relations between the quasi-periodic wave solutions and soliton
solutions are rigorously established. It is shown that the soliton solutions
can be obtained only as limiting cases of the quasi-periodic wave solutions
under small amplitude limits in superspace $\mathbb{R}_\Lambda^{2,1}$. We find
that, in contrast to the purely bosonic case, there is an interesting
influencing band occurred among the quasi-periodic waves under the presence of
the Grassmann variable. The quasi-periodic waves are symmetric about the band
but collapse along with the band. Furthermore, the amplitudes of the
quasi-periodic waves increase as the waves move away from the band. The
efficiency of our proposed method can be demonstrated on a class variety of
supersymmetric equations such as those considered in this paper,
$\mathcal{N}=1$ supersymmetric KdV, Sawada-Kotera-Ramani and Ito's equations,
as well as $\mathcal{N}=2$ supersymmetric KdV equation.
