  Context. The formation of water on the dust grains in the interstellar medium
may proceed with hydrogen peroxide (H2O2) as an intermediate. Recently
gas-phase H2O2 has been detected in {\rho} Oph A with an abundance of ~1E-10
relative to H2.
  Aims. We aim to reproduce the observed abundance of H2O2 and other species
detected in {\rho} Oph A quantitatively.
  Methods. We make use of a chemical network which includes gas phase reactions
as well as processes on the grains; desorption from the grain surface through
chemical reaction is also included. We run the model for a range of physical
parameters.
  Results. The abundance of H2O2 can be best reproduced at ~6E5 yr, which is
close to the dynamical age of {\rho} Oph A. The abundances of other species
such as H2CO, CH3OH, and O2 can be reasonably reproduced also at this time. In
the early time the gas-phase abundance of H2O2 can be much higher than the
current detected value. We predict a gas phase abundance of O2H at the same
order of magnitude as H2O2, and an abundance of the order 1E-8 for gas phase
water in {\rho} Oph A. A few other species of interest are also discussed.
  Conclusions. We demonstrate that H2O2 can be produced on the dust grains and
released into the gas phase through non-thermal desorption via surface
exothermic reactions. The H2O2 molecule on the grain is an important
intermediate in the formation of water. The fact that H2O2 is over-produced in
the gas phase for a range of physical conditions suggests that its destruction
channel in the current gas phase network may be incomplete.
