In wireless broadcast environments, a system performance can be improved with random linear network coding (RLNC). In RLNC, a source transmits a set of coding coefficients and a coded packet together. The coded packet is a combination of the coding coefficients and uncoded packets. Using the key feature of RLNC, we herein propose a new RLNC scheme to minimize outage probability with a feedback channel. In addition, the outage probability of the proposed scheme is analyzed in a Rayleigh fading channel. Through the numerical analysis and Monte Carlo simulations, we demonstrate that the outage probability of the proposed scheme is lower than that of a conventional RLNC scheme.