It is noted that in the new Particle Data Group (PDG) version the rare decays of the Λb baryon have been revised with more accuracy.The new.results show that most of the existing theoretical results on the process Λb → Λγ are larger than those of experiments.With the improved higher-order light-cone distribution amplitudes of the Λ baryon,we reanalyze the process in the framework of light-cone quantum chromodynamics sum rules and the branching ratio is estimated to be Br(Λb → Λγ) =(7.38+0.40-0.39) × 10-6,which is consistent with the new experimental result.Furthermore,another process Λb →Λ l+l-is also analyzed in the same frame.The final branching ratio is calculated to be Br(Λb → Λl+l-) =1.20 × 10-6,which is in good accordance with the data from the PDG and other theoretical predictions.