A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles indicating the presence of a relativistic accretion disk model. Using a Monte Carlo technique, we compute the linear polarization of a double peaked broad emission line. A Keplerian accretion disk is adopted for the double peak emission line region and the Schwarzschild geometry is assumed in the emission region. Far from the accretion disk where flat Minkowski geometry is appropriate, we place a scattering region in the shape of a spherical shell sliced. We generate a line photon in the accretion disk in an arbitraray direction in the local rest frame and follow the geodesic of the photon until it hits the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the linear degree of polarization also shows a double peak structure. Under a favorable condition we show that up to 1% of linear degree of polarization may be obtained.