A channeled spectropolarimeter (CSP) measures spectrally resolved Stokes parameters from a snapshot. However, the reconstruction of Stokes parameters may suffer from noise and systemic errors, lowering the measurement accuracy. To accurately reconstruct Stokes parameters from the experimental data with random noise and residual systematic errors after calibration, we propose an adaptive linear reconstruction with regularizer (ALRR) for CSP. By modeling an l1-norm optimization problem with a 1-norm regularizer consisting of coefficients from the Legendre polynomials basis, together with an adaptive residual threshold considering the systematic errors and noise, Stokes parameters are reconstructed accurately in the presence of noise and systemic errors. Simulation results demonstrate the efficiency and noise-robustness of ALRR with a signal-to-noise ratio of 12 dB, while its self-adaption and accuracy are validated experimentally with a root-mean-square error of   <  0.04. The proposed method can have important potential in real-time polarization measurement and processing for modulated polarimeters (i.e., Stokes CSP and Mueller CSP).