High transition temperature (high-Tc) superconducting quantum interference devices (SQUIDs) based on bicrystal grain boundary junctions have been utilized in a wide range of applications. To explore the effect of the bicrystal grain boundary angle on the property of the high-Tc SQUID, we fabricated and characterized YBa2Cu3O7−δ (YBCO) radio frequency (rf) SQUIDs using [001]-tilt grain boundary junctions on SrTiO3 (STO) bicrystal substrates with three different misorientation angles of θ=18∘, 24°, and 30°. Unlike the device of θ=18∘ showing only the triangular waveform of the voltage–flux (V−Φ) characteristics, for device of θ=24∘ and 30°, the shape of the V−Φ curve can be tuned from approximately triangular into nearly rectangular by adjusting the working point of the device. It suggests that, as θ increases from 18° to 30°, the operation of the device may change from the hysteretic mode into the nonhysteretic mode. This is backed by electrical transport measurements of YBCO bicrystal junctions on separate STO substrates, which help to reveal that lying behind the indicated changeover of the SQUID operation mode is the exponential decrease of the junction critical current density Jc as θ increases. The white noise of the device, which decreases with increasing flux-to-voltage transfer coefficient ∂V/∂Φ, shows a large drop as θ increases to 24°. For both 24° and 30° devices, the white field noise at 77 K is about 90 fT/Hz1/2 at respective optimum working points. For device of 30° with nearly rectangular V−Φ characteristics showing the largest ∂V/∂Φ among the fabricated samples, the white noise region extends below 10 Hz and a field noise of 145 fT/Hz1/2 at 1 Hz is shown, demonstrating the potential of obtaining high-performance bicrystal YBCO rf SQUIDs with this grain boundary angle.