Copper is a well known alloying element that is used to improve the resistance to general corrosion of stainless steel And also Cu cation have the anti-fouling effect to inhibit adhesion of the marine algae and shellfish to the surface of heat exchanger cooling pipe or outside wall of the ship, Therefore there are some anti-fouling methods such as anti-fouling Paint mixed with copper oxide or MGPS(Marine Growth Preventing System) by using Cu cation dissolved to the sea wather solution. Cu cation can be dissolved spontaneously by galvanic current due to Potential difference between Cu and cooling pipe of heat exchanger with Ti material, which may be one of the anti-fouling designs. In this study the effect of annealing heat treatment to galvanic current and Polarization behavior was investigated with a electrochemical points of view such as measurement of corrosion Potential, anodic polarization curve. cyclic voltammetric curve, galvanic current etc The grain size of the surface in annealed at $700^{circ}C$ was the smallest than that of other annealing temperatures. and also the corrosion Potential showed more positive potential than other annealing temperatures. The galvanic current between Ti and Cu with annealed at $700^{circ}C$ was the largest value in the case of static condition. However its value in the case of flow condition was the smallest than the other temperatures. Therefore in order to increase anti-fouling effect by Cu cation, the optimum annealing temperature in static condition of sea water is $700^{circ}C$, however non- heat treated specimen in the case of flow condition may be desirable