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Non-Gaussian statistic model, alpha stable distribution has gained much attention due to its generality to represent heavy-tailed and impulsive interference. Unfortunately, there is no closed form expression for the probability density function of alpha-stable distributions. Hereby, to develop the approximate expressions is of importance for signal detection and denoising. This paper is concerned with the weak signal detection in α-stable interference. We present a novel approximate expression that is a simplified version of Cauchy-Gaussian mixture (CGM) for symmetric α-stable (SαS) distribution. Consequently, the non-linearity limiter of locally optimal (LO) detector is deduced. Compared with Cauchy detector, the proposed detector has near optimal performance.