For the physical layer security communication scenario in double-layer satellite networks consisting of geostationary earth orbit （GEO） satellite and low earth orbit （LEO） satellite cluster， we propose a robust secure beamforming （BF） algorithm based on Lagrange multiplier method under the condition that only the imperfect channel state information （CSI） of the eavesdropper is known. LEO satellite clusters， acted as relays， adopt amplification and forwarding protocols to assist GEO satellite in serving the ground legitimate user. An eavesdropper on the ground tries to steal the satellite signal. Firstly， a joint optimization problem is formulated to maximize the signal-to-noise ratio of the ground legitimate user while satisfying the intercept probability （IP） constraint of the eavesdropper and the maximum transmit power constraint of the GEO satellite. Secondly， we use the matrix transformation method and the cumulative density function of the exponential distribution to transform the complex nonconvex IP constraint into convex one. Thirdly， using Lagrange multiplier method， we attain the transmit power of GEO satellite and the closed-form solution to the distributed BF weight vector of LEO satellite clusters in an efficient way. The simulation results show that the proposed algorithm can guarantee the secure communication of the considered double-layer satellite network under different channel errors， verifying the effectiveness of the algorithm in secure transmission and its robustness to channel errors.