Mode selection is crucial for a stable single-mode oscillation of an optoelectronic oscillator (OEO). In this paper a parity-time (PT)-symmetric frequency-tunable OEO is proposed and experimentally demonstrated, to realize precise frequency tuning without using any narrowband filter. The proposed PT-symmetric OEO is implemented based on two identical optoelectronic hybrid loops mainly consisting of a shared dual-parallel Mach-Zehnder modulator (DPMZM) and a photodetector. The PT-symmetry condition can be achieved by enabling antisymmetric gain/loss in the two loops through manipulating the bias voltages of the two child-MZMs of DPMZM, and continuous frequency tunability is realized by adjusting the bias voltage of the parent-MZM. A theoretical model is developed for the proposed PT-symmetric OEO to analyze the dynamics of the PT-supermodes as the gain/loss coefficient changing. Furthermore, an experiment is performed. Without high-Q filter, stable single-mode oscillation of the PT-broken supermode at 4.2 GHz with side-mode suppression ratios of 60 and 50 dB is demonstrated in the OEO with 6 and 2000 m fiber loop lengths, respectively. The frequency tuning ranges are 1.4 MHz and 1.5 kHz for two OEOs with different fiber loop lengths.