We report on the electrical-to-optical modulation bandwidths of non-mesa-etched semipolar (112¯2) InGaN/GaN light-emitting diodes (LEDs) operating at 430-450 nm grown on high-quality (112¯2) GaN templates, which were prepared on patterned (101¯2) r-plane sapphire substrates. The measured frequency response at -3 dB of the LEDs was up to 1 GHz. A high back-to-back data transmission rate of above 2.4 Gbps is demonstrated using a non-return-to-zero on-off keying modulation scheme. This indicates that (112¯2) LEDs are suitable gigabit per second data transmission for use in visible-light communication applications.