Time-resolved optical measurements in (110)-oriented GaAs/AlGaAs quantum wells show a ten-fold increase of the spin-relaxation rate as a function of applied electric field from 20 to 80 kV cm-1 at 170 K and indicate a similar variation at 300 K, in agreement with calculations based on the Rashba effect. Spin relaxation is almost field-independent below 20 kV cm-1 reflecting quantum well interface asymmetry. The results indicate the achievability of voltage-gateable spin-memory time longer than 3 ns simultaneously with high electron mobility.