  We present the locally supersymmetric formulation of unimodular gravity
theory in D (1\le D \le 11) dimensions, namely supergravity theory with the
metric tensor whose determinant is constrained to be unity. In such a
formulation, the usual fine-tuning of cosmological constant is no longer
needed, but its value is understood as an initial condition. Moreover, the
zero-ness of the cosmological constant is concluded as the most probable
configuration, based on the effective vacuum functional. We also show that the
closure of supersymmetry gauge algebra is consistent with the unimodular
condition on the metric.
