We have found and analysed 16 multipeaked type-I bursts from the neutron-star low-mass X-ray binary 4U 1636 - 53 with the Rossi X-ray Timing Explorer (RXTE). One of the bursts is a rare quadruple-peaked burst that was not previously reported. All 16 bursts show a multipeaked structure not only in the X-ray light curves but also in the bolometric light curves. Most of the multipeaked bursts appear in observations during the transition from the hard to the soft state in the colour-colour diagram. We find an anticorrelation between the second peak flux and the separation time between two peaks. We also find that in the double-peaked bursts the peak-flux ratio and the temperature of the thermal component in the pre-burst spectra are correlated. This indicates that the double-peaked structure in the light curve of the bursts may be affected by enhanced accretion rate in the disc, or increased temperature of the neutron star.