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We introduce a new kind of super warped product spaces$\bar{M}_{_{(I)}}=\textbf{I}^{1|0}\times_f M^{m|n}$,$\bar{M}_{_{(II)}}=\textbf{I}^{0|1}\times_{f} M^{m|n}$, and$\bar{M}_{_{(III)}}=\textbf{I}^{1|1}\times_{f} M^{m|n}$, where $M^{m|n}$ is asupermanifold of dimension $m|n$, $\textbf{I}^{\delta|\delta'}$ is standardsuperdomain with $\textbf{I}=(0,1)$ and $\delta,\delta' \in \{0,1\}$, subjectto the warp functions $f(t)$, $f(\bar t)$, and $f(t, \bar t)$, respectively. Ineach super warped product space, $\bar{M}_{_{(I)}}$, $\bar{M}_{_{(II)}}$, and$\bar{M}_{_{(III)}}$, it is shown that Einstein equations$\bar{G}_{AB}=-\bar{\Lambda}\bar{g}_{AB}$, with cosmological term$\bar{\Lambda}$ are reducible to the Einstein equations $G_{\alpha\beta} =-\Lambda g_{\alpha\beta}$ on the super space $M^{m|n}$ with cosmological term${\Lambda}$, where $\bar{\Lambda}$ and ${\Lambda}$ are functions of $f(t)$,$f(\bar t)$, and $f(t, \bar t)$, as well as ($m$, $n$). This dependence pointsto the origin of cosmological terms which turn out to be within the warpedstructure of the super space-time. By using the Generalized Robertson-Walkerspace-time, as a super space-time, and demanding for constancy of$\bar{\Lambda}$ we can determine the warp functions and $\Lambda$ which resultin finding the solutions for Einstein equations$\bar{G}_{AB}=-\bar{\Lambda}\bar{g}_{AB}$ and $G_{\alpha\beta} = -\Lambdag_{\alpha\beta}$. We have discussed the cosmological solutions, for each kindof super warped product space, in the special case of $M^{3|0}$.

Einstein equations with cosmological constant in Super Space-Time