We investigate the doping dependence of flux pinning in superconducting NaFe1-xCoxAs (x = 0.01, 0.03, 0.05 and 0.07) single crystals grown by the Bridgman method. The electronic specific heat displays a pronounced anomaly in a sample series at superconducting transition temperature, which hardly shows any residual part at low temperature. We found that Co doping plays an important role in signifying the secondary peak in the magnetic hysteresis of optimally doped (x = 0.03) and heavily doped (x = 0.05, 0.07) crystals. Furthermore, the dependence of the relaxation rate S = vertical bar d lnM / d ln t vertical bar on magnetic field and temperature exhibits a decreasing trend within a certain range corresponding to the secondary peak effect in the optimally and heavily doped samples. The magnetic relaxation rate combined with the Maley analysis of the current-dependent creep energy shows a single-vortex pinning in the lightly doped sample dominant at low applied fields, and plastic pinning at high applied fields, without showing a secondary peak. However, in the optimally and heavily doped samples, the magnetic relaxation rate and U(J) isothermal analysis show that the collective pinning that dominates below H-peak crosses over to plastic pinning for fields above H-peak.