Superconductivity stabilization and enhancement of the Bi2 Sr2CuO6-δ-type (2021) phase was reported through partial replacement of La^3+ ions for Sr^2+ ions. Superconductivity transition temperature with T, (resistivity zero) up to 19 K, Tc(midpoint) of 27 K and onset around 35 K was obtained for compound Bi2(Sr1.5 La0.5)CuO6-δ. Low room temperature electrical resistivity and bulk Meissner signal (field-cooled) were observed for the single phase Bi2(Sr2-xLax)CuO6-δsystem (0.0 < x < 1.0) except near the phase boundary. The stabilization and enhancement of superconductivity is probably attributed from the different valency between La^3+ions and Sr^2+ ions, which plays the role of electron donors and thus the oxygen attraction centers. Pairing field energy of 2 10 K and electron-elementary excitation coupling constant h of 0.50 were derived from BCS-like Tc formula through comparing with other Bi systems Bi2Can-1Sr2CunO2n+4-δ(n = 1,2,3).