Abstract: A model is presented for computing the array gain of circular array surrounding on a rigid sphere baffle through calculating the noise cross spectral matrix accurately.Then based on the array gain calculating model,a robust supergain beamforming method via second-order cone programming in mode space is proposed.In this method,the robust weighting vector in sensor space is transformed into robust coefficients vector in mode space according to the concept of phase modes,therefore designing robust supergain under different mode orders is available.Since the white noise constraint and low mode orders under low frequencies are adopted,the method solves the weak robustness problem of supergain beamformer especially at low frequencies.Results of computer simulation indicated that this method can provide more robust beamforming schemes and more suitable compromise among multiple beam performance parameters than both conventional method and robust beamforming method in sensor space simultaneously.