We present the analysis of 510 light curves in V and I bands of 255 giant stars in the globular cluster NGC-3201. Our aim is to expand the sample of new types of variables reported in a previous study. These variables show a short period (PV<0.6day) and a low amplitude (AV<0.06mag.). We first searched for variability using the generalized Lomb-Scargle and phase dispersion minimization periodograms of the sample, discarding 167 stars as non-variables. We then applied the significance test and reduced the sample to 88 giants, of which we classified 18 as possible variables, 11 as dubious, 41 as non-variables, and 18 as variables. We finally determined the cluster membership of this sample and grouped each star based on their light-curve shape. The discovered variables show periods in the range 0.2440<PV<0.5868days and amplitudes between 0.010<AV<0.064 mag. Within the sample of 18 variable stars, we report the discovery of an object with a period PV=0.3603{+/-}0.0012 and amplitude AV=0.703{+/-}0.029 mag that shows a RR-Lyrae ab-type light curve. Additionally, we report two RR-Lyrae ab and c types with ultralow amplitude.