In this paper, the belief propagation (BP) based approximation methods which are introduced for low density parity check (LDPC) codes in literature are adapted to the Raptor decoder structure in order to reduce its computational complexity. The bit error rate (BER) performances of the algorithms over the additive white Gaussian noise (AWGN) channel are obtained by both theoretical works and simulations. The Monte-Carlo based density evolution (MC-DE) method is used for theoretical analysis. In addition to this, computational complexity analyses of the considered methods are presented. Results show that the computational complexity can be significantly decreased with a limited performance loss cost.