PURPOSE: We calculated the dosimetric indices and estimated the tumor control probability (TCP) considering six degree-of-freedom (6DoF) patient setup errors in stereotactic radiosurgery (SRS) using a single-isocenter technique. METHODS: We used simulated spherical gross tumor volumes (GTVs) with diameters of 1.0 cm (GTV 1), 2.0 cm (GTV 2), and 3.0 cm (GTV 3), and the distance (d) between the target center and isocenter was set to 0, 5, and 10 cm. We created the dose distribution by convolving the blur component to uniform dose distribution. The prescription dose was 20 Gy and the dose distribution was adjusted so that D95 (%) of each GTV was covered by 100% of the prescribed dose. The GTV was simultaneously rotated within 0°-1.0° (δR) around the x-, y-, and z-axes and then translated within 0-1.0 mm (δT) in the x-, y-, and z-axis directions. D95, conformity index (CI), and conformation number (CN) were evaluated by varying the distance from the isocenter. The TCP was estimated by translating the calculated dose distribution into a biological response. In addition, we derived the x-y-z coordinates with the smallest TCP reduction rate that minimize the sum of squares of the residuals as the optimal isocenter coordinates using the relationship between 6DoF setup error, distance from isocenter, and GTV size. RESULTS: D95, CI, and CN were decreased with increasing isocenter distance, decreasing GTV size, and increasing setup error. TCP of GTVs without 6DoF setup error was estimated to be 77.0%. TCP were 25.8% (GTV 1), 35.0% (GTV 2), and 53.0% (GTV 3) with (d, δT, δR) = (10 cm, 1.0 mm, 1.0°). The TCP was 52.3% (GTV 1), 54.9% (GTV 2), and 66.1% (GTV 3) with (d, δT, δR) = (10 cm, 1.0 mm, 1.0°) at the optimal isocenter position. CONCLUSION: The TCP in SRS for multiple brain metastases with a single-isocenter technique may decrease with increasing isocenter distance and decreasing GTV size when the 6DoF setup errors are exceeded (1.0 mm, 1.0°). Additionally, it might be possible to better maintain TCP for GTVs with 6DoF setup errors by using the optimal isocenter position.