Experimental result and theoretical analysis are reported for bias-voltage dependence of oscillation frequency in resonant tunneling diodes (RTDs) integrated with slot antennas. Frequency change of 18 GHz is obtained experimentally for a device with the central oscillation frequency of 470 GHz. The observed frequency change is attributed to the bias-voltage dependence of the transit time of electrons across the RTD layers, which results in a voltage-dependent capacitance added to RTD. Theoretical analysis taking into account this transit time is in reasonable agreement with the observed results. Voltage-controlled RTD oscillators in the terahertz range are expected from the theoretical results. A structure suitable for large frequency change is also discussed briefly.