The Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory detected gamma-ray bursts (GRBs) with a real-time burst detection (or trigger) system running onboard the spacecraft. Under some circumstances, however, a GRB may not have activated the onboard burst trigger. For example, the burst may have been too faint to exceed the onboard detection threshold, or it may have occurred while the onboard burst trigger was disabled for technical reasons. This paper describes a catalog of 873 non-triggered GRBs that were detected in a search of the archival continuous data from BATSE, recorded between 1991 December 9.0 and 1997 December 17.0. For each burst, the catalog gives an estimated source direction, duration, peak flux, and fluence. Similar data are presented for 50 additional bursts of unknown origin that were detected in the 25--50 keV range; these events may represent the low-energy tail of the GRB spectral distribution. This catalog increases the number of GRBs detected with BATSE by 48% during the time period covered by the search.