A numerical study on spin-polarized transport properties in a quasi-one-dimensional wire with Rashba quantum dots is presented. The ballistic spin transmission probability and spin density profiles are obtained using the quantum transmitting boundary method. The Fano-Rashba effect on the spin transmission is analyzed as a function of the Rashba spin-orbit coupling strength for single dot and double dot systems. The spin density profiles show the localized states that contribute to the backscattering and spin-flip processes in the Rashba dots. The results enlighten us on the Fano-Rashba effect caused by local Rashba spin-orbit coupling and provide concrete ideas for modeling a system with spin-polarized transport for future applications.