  We present a novel, fast and precise method for including the effect of light
neutrinos in cosmological N-body simulations. The effect of the neutrino
component is included by using the linear theory neutrino perturbations in the
calculation of the gravitational potential in the N-body simulation. By
comparing this new method with the full non-linear evolution first presented in
\cite{Brandbyge1}, where the neutrino component was treated as particles, we
find that the new method calculates the matter power spectrum with an accuracy
better than 1% for \sum m_\nu \lesssim 0.5 eV at z = 0. This error scales
approximately as (\sum m_\nu)^2, making the new linear neutrino method
extremely accurate for a total neutrino mass in the range 0.05 - 0.3 eV. At z =
1 the error is below 0.3% for \sum m_\nu \lesssim 0.5 eV and becomes negligible
at higher redshifts. This new method is computationally much more efficient
than representing the neutrino component by N-body particles.
