We present the field and temperature dependence of the magnetizations of BaFe 1.9 Pt 0.1 As 2 and Ba 0.95 La 0.05 Fe 1.9 Pt 0.1 As 2 samples synthesized by solid-state reaction method.The samples were formed as a single phase in the ThCr 2 Si 2 -type structure. Replacing Ba with the smaller La atom results in a lattice shrinkage. The critical current, J c (H, T) has been determined (using Bean's critical state model) from magnetic hysteresis loops in a temperature range between T = 5 K and the superconducting transition temperatures (20 K), in fields up to H = 9 T. We find a nonmonotonic 'fishtail' shape (exhibiting a second peak) of the magnetization loops as well as a very large irreversibility. We observe a remarkable flux jump at T = 5 K for BaFe 1.9 Pt 0.1 As 2 due to magneto-thermal instability, but a very sharp magnetization peak for Ba 0.95 La 0.05 Fe 1.9 Pt 0.1 As 2 near H = 0, which corresponds to a much-reduced relaxation rate of vortices. J c decreases exponentially with temperature as well as with field in lower temperatures and fields ranges. La doping causes a considerable increase in the irreversibility, leading to a significant enhancement of J c . The analysis shows that the high J c is mainly due to collective (weak) pinning of vortices by dense microscopic point defects with some contribution from a strong pinning mechanism.The normalized pinning force F p /F p,max as a function of the reduced magnetic field h = H/H irr is also obtained. Using the approaches of Dew-Hughes (1974 Phil. Mag. 30 293) and Kramer (1973 J. Appl. Phys. 44 1360, we determine the nature of the pining sources. It is found that many different pinning mechanisms are active simultaneously. The modified expression of F p /F p,max based on collective pinning theory enables us to determine the field dependence of the relaxation rate S(H, T = 5 K) indirectly instead of using more difficult relaxation measurements.Finally, all drastic changes with La doping are clearly demonstrated and investigated under different models introduced in the literature.