A covert communication system using a random carrier having skewed α‐stable distribution is introduced. The proposed method utilises the random signals with skewed α‐stable distributions exhibiting antipodal characteristics to encode the binary information at the transmitter. The receiver recovers these positive and negative skewed α‐stable distributed random signals by switching at different time instants, where only the receiver has the correct switching order. The third‐order statistic, given as sample skewness, is used to determine the message inside the receiver structure. The main purpose of constructing such a communication system is to improve the security aspect by avoiding the self‐repeating autocorrelation behaviour of the transmitted signal in the time domain. The improvement of security is shown by comparing the fractional lower‐order covariance with the reference study. According to the bit error rate results, the proposed method also shows better performance when the impulsiveness of the random carrier having skewed stable distribution is increased.