Electrospun nanofiber is regarded as a promising candidate for many high-end applications due to its advantageous unique structure. Ultrafine fiber and good mechanical property are essential to ensure its performance. In this work, tunable ultrafine diameter and significantly enhanced mechanical strength of electrospun Styrene-butadiene-styrene tri-block copolymer (SBS) membrane are attained by means of the addition of LiBr into SBS solution dissolved in tetrahydrofuran/dimethylformamide (THF/DMF). Solution conductivity is found to grow in two steps with the increasing lithium bromide (LiBr) concentration and a critical point is observed at the ultralow concentration of 0.005 wt%, sharp increase below it but modest increase above it. Interestingly, the diameter of electrospun fiber shows a significant reduction with increase of LiBr concentration below this critical point but minor fluctuation above this. Welded structure is observed between adjacent fibers and the degree of welding goes deeper with increase of salt concentration. Accordingly, the mechanical strength of electrospun membrane is gradually enhanced and reaches to the highest value of 5.7 MPa at the critical concentration, with enhancement of 134% in comparison with pure electrospun SBS membrane, and then declines when further adding LiBr. TEM observation confirms more oriented and distinct self-assembly domains in the finer fibers, which contribute greatly to the property enhancement for electrospun SBS membrane obtained below critical concentration. The finding of critical concentration is important for the preparation of high performance electrospun membrane by adding salt in the spinning solution.