Highway travel time is a critical performance measure. This information is important to carriers and shippers to schedule deliveries and plan activities. Past studies have increasingly relied on GPS data to estimate travel time because of the great spatial coverage and the growing availability of the data. However, public GPS data usually report locations and time stamps with a low frequency for proprietary concerns. Sparse location data present challenges for the estimation of travel speed and time, because trip information collected from two consecutive reported locations only reflects aggregate traffic conditions of the traversed highway links on the route. The ordinary least squares method provides a starting point for estimating travel time on each individual link from trip travel time, but this method is sensitive to the variance of vehicle travel speed on a link and is likely to produce volatile estimates. To obtain an accurate speed and time estimate on each link, the proposed regularized regression model maximizes the likelihood of obtaining the observed trip travel time while also alleviating extra volatility in speed estimates. The performance of the model is evaluated with sparse vehicle location data simulated from actual corridor loop detector data. The model is proved capable of recovering a true speed plot of the corridor. A closer examination of the link travel time allocated on the basis of speed estimates shows that the method improves significantly on benchmark link travel time allocation, particularly in congested areas or on links with great variance of speed.