We searched for 10 TeV burst-like events coincident with the BATSE bursts in the Tibet air-shower dataset. The data taken during the period of June 18, 1990 through September 29, 1992 were used for this analysis. During this period, 57 bursts in the 2B BATSE catalog were located in the effective viewing sky of our array. In this study we introduced a clustering technique to find burst-like events preferentially. It is shown that this technique is a valid alternative to other burst search methods. No convincing signal was detected at the trigger time and from the direction of any BATSE bursts. However, when the burst-like events coming from the directions within a 1 sigma BATSE location error box are superimposed on all the durations ranging from 1 to 100 seconds, the resulting probability distribution shows a deviation from the background with a statistical significance of the order of 6 sigma. Further observation with our new array, being fully operated at a trigger rate of about 250 Hz, is expected to confirm this interesting result with improved statistics in the near future and will enable reliable investigation on the nature of gamma-ray bursts.