In this paper, we introduce a novel modulation recognition method of digital communication signals with alpha-stable noise to solve the problem of low recognition performance in mixed signal-to-noise-ratio environment. The received signals are separated into signals and alpha-stable noise by employing fractional lower order fast independent component analysis (FLO-Fast-ICA), and then the separated signals are interpolated based on the global average local mean decomposition. With these processing, two classification features that are the segmented instantaneous frequency standard deviation and the segmental instantaneous amplitude standard deviation are extracted. Thereafter, a decision tree classifier is developed to recognize the digital communication signals including minimum shift keying (MSK), 2 amplitude shift keying (2ASK), quadrature phase shift keying (QPSK) and 16 quadrature amplitude modulation (16QAM). Simulation results show that the proposed method has a promising performance without prior information.