Photonics-based radar with a photonic de-chirp receiver has the advantages of broadband operation and real-time signal processing, but it suffers from interference from image frequencies and other undesired frequency-mixing components, due to single-channel real-valued photonic frequency mixing. In this paper, we propose a photonics-based radar with a photonic frequency-doubling transmitter and a balanced in-phase and quadrature (I/Q) de-chirp receiver. This radar transmits broadband linearly frequency-modulated signals generated by photonic frequency doubling and performs I/Q de-chirping of the radar echoes based on a balanced photonic I/Q frequency mixer, which is realized by applying a 90° optical hybrid followed by balanced photodetectors. The proposed radar has a high range resolution because of the large operation bandwidth and achieves interference-free detection by suppressing the image frequencies and other undesired frequency-mixing components. In the experiment, a photonics-based K-band radar with a bandwidth of 8 GHz is demonstrated. The balanced I/Q de-chirping receiver achieves an image-rejection ratio of over 30 dB and successfully eliminates the interference due to the baseband envelope and the frequency mixing between radar echoes of different targets. In addition, the desired de-chirped signal power is also enhanced with balanced detection. Based on the established photonics-based radar, inverse synthetic aperture radar imaging is also implemented, through which the advantages of the proposed radar are verified.