  We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an
arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's
parameter $\beta$. This generalized Lagrangian involves the chiral one as a
special case of the value $\xi = \pm i$. We show that the generalized
Lagrangian gives the canonical formulation of N = 1 SUGRA with the real
Ashtekar variable after the 3+1 decomposition of spacetime. This canonical
formulation is also derived from those of the usual N = 1 SUGRA by performing
Barbero's type canonical transformation with an arbitrary parameter $\beta
(=\xi^{-1})$. We give some comments on the canonical formulation of the theory.
