A low cost frequency-dependent (FD) I/Q imbalance self-compensation scheme is investigated in this paper. The direct conversion transmitters are widely used in wireless systems. However, the unwanted image-frequencies and distortions are inevitably introduced into the direct conversion system. This problem is even severer in wideband systems. Therefore, the accurate estimation and compensation of I/Q imbalance is crucial. The current compensation method is based on external instruments or internal feedback path which introduces additional impairments and is expensive. This paper proposes a low cost FD I/Q imbalance self-IQ-demodulation based compensation scheme without using external calibration instruments. First, the impairments of baseband and RF components are investigated. Further, I/Q imbalance model is developed. Then, the proposed a self-IQ-demodulation based compensation scheme is investigated. The overall FD I/Q imbalance parameters are estimated by developing a self-IQ-demodulation algorithm. To realize this self-IQ-demodulation algorithm, this paper introduces minor modifications to the current power detector circuit and specially designed training signal. Afterwards, the estimated parameters are applied to the baseband equivalent compensator. This sophisticated algorithm guarantees low computation complexity and low cost. The compensation performance is evaluated in laboratory measurement.