Timing measurements with silicon photomultipliers (SiPMs) are affected by the major issue of the so-called time-walk effect; this is due to the intrinsic architecture of SiPM devices. A new technique for time-walk compensation in timing measurements with SiPMs is presented and discussed, feasible with a low-complexity and low-cost circuitry and able to improve the timing accuracy. The validity of the presented technique has been experimentally proven with a 3 x 3 mm(2) Hamamatsu MPPC, achieving a jitter reduction of a factor 2.85 compared with the case without time-walk compensation. To perform the experimental validation, a discrete-components transimpedance amplifier is developed with large bandwidth and low jitter, specifically designed to read-out and amplify the SiPM signal.