  We derive the equations of motion of type II 4D supergravity in superspace.
This is achieved by coupling the Type II Berkovits' hybrid superstring to an
N=2 curved background and requiring that the sigma-model has N=(2,2)
superconformal invariance at one loop. We show that there are no anomalies in
the fermionic OPE's and the complete set of compensator's equations is derived
from the energy-momentum tensor. The equations of motion describe a
hypertensorial and vectorial multiplet coupled to a U(1)\times U(1) N=2
Poincar\`e Supergravity.
