  We construct the off-shell recursion for gravity and the graviton current for
the perturbative double field theory (DFT). We first formulate the perturbative
DFT, which is equivalent but simpler to perturbative general relativity, to
all-orders in fluctuations of generalised metric. The perturbative action and
equations of motion (EoM) are derived to arbitrary order for pure gravity case.
We then derive the graviton off-shell recursion, the gravity counterpart of the
Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner
method using the EoM of the perturbative DFT. We solve the recursion
iteratively and obtain the graviton off-shell currents explicitly. We then
discuss the classical double copy for the off-shell currents. We present the
current KLT relation for gravity by extending the result proposed by Mizera and
Skrzypek for the non-gravitational effective field theories. The relation
represents graviton currents by squaring gluon currents with the KLT kernel up
to gauge transformation and regular terms that do not have any pole. Finally we
discuss the off-shell conservation of currents for nonlinear gauge choices.
