T(1ρ) relaxation is traditionally described as a mono-exponential signal decay with spin-lock time. However, T(1ρ) quantification by fitting to the mono-exponential model can be substantially compromised in the presence of field inhomogeneities, especially for low spin-lock frequencies. The normal approach to address this issue involves the development of dedicated composite spin-lock pulses for artifact reduction while still using the mono-exponential model for T(1ρ) fitting. In this work, we propose an alternative approach for improved T(1ρ) quantification with the widely-used rotary echo spin-lock pulses in the presence of B(0) inhomogeneities by fitting to a modified theoretical model which is derived to reveal the dependence of T(1ρ)-prepared magnetization on T(1ρ), T(2ρ), spin-lock time, spin-lock frequency and off-resonance, without involving complicated spin-lock pulse design. It has potentials for T(1ρ) quantification improvement at low spin-lock frequencies. Improved T(1ρ) mapping was demonstrated on phantom and in vivo rat spin-lock imaging at 3 T compared to the mapping using the mono-exponential model.