The direction-of-arrival (DoA) estimation from spherical microphone array data requires mode strength compensation for removing the dependency on the array surface impedance. However, in practice, mismatches exist in the actual and modeled surface impedances and degrade the DoA estimation performance. Herein, a non-parametric beamformer that can accurately estimate DoAs under the mode strength mismatch is proposed. The technique utilizes a block-diagonal covariance matrix and order-dependent normalization of spherical harmonic coefficients. The proposed method tested for various surface impedance mismatches and DoAs shows robust estimation performance with reduced dependency on the array surface impedance.