Role of the Λ(1600) is studied in the K-p → Λπ0π0 reaction by using the effective Lagrangian approach near the threshold.We perform a calculation for the total and differential cross sections by considering the contributions from the Λ(1600) and Λ(1670) intermediate resonances decaying into π0Σ*0(1385) with Σ*0(1385) decaying into π0Λ.Additionally,the non-resonance process from u-channel nucleon pole is also taken into account.With our model parameters,the current experimental data on the total cross sections of the K-p → Λπ0π0 reaction can be well reproduced.It is shown that we really need the contribution from the Λ(1600) with spin-parity JP =1/2+,and that these measurements can be used to determine some of the properties of the Λ(1600) resonance.Furthermore,we also plot the π0Λ invariant mass distributions which could be tested by the future experimental measurements.