In this paper a new algorithm for short-term regularized estimation of vertical total electron content (VTEC) from Global Positioning System (GPS) data is developed. The regularization technique can combine signals, from all GPS satellites for a given instant and a given receiver, for a desired time duration within the 24 hour period without missing any important features in the temporal domain. The algorithm is based on the minimization of a cost function which includes a high pass penalty filter and detrend processing. With an optional weighting function the multipath effects are reduced. A final sliding window median filter is added to enrich the processing and smoothing of the data. The developed regularized estimation algorithm is applied to GPS data for various locations for the solar maximum week of 23--28 April 2001. The parameter set that is required by the estimation algorithm is chosen optimally using appropriate error functions. For this data set the chosen robust and optimum parameters can be used for all latitudes and for both quiet and disturbed days for a minimum of one hour time period. It is observed that the estimated TEC values are in very accordance with the TEC estimates for the 24 hour period. Owing to its 30 s time resolution, the regularized VTEC estimates from the developed algorithm are very successful in representation and tracking of sudden temporal variations of the ionosphere, especially for high latitudes and during ionospheric disturbances.