detecting the subject by performing a preview mode in a camera mode;

detecting and storing a focus value while moving the lens according to a distance between the detected subject and the lens, determining based on a presently-detected focus value and a previously-stored focus value if a slope has changed, and detecting an optimum focus value from a focus value at which the slope has changed;

performing a tracking mode to track a focus in a predetermined zone which comprises the detected optimum focus value;

comparing a first resultant value obtained by subtracting a first previous focus value from a first presently-detected focus value with a first threshold value, the first presently-detected focus value being detected by increasing electrical current by a first predetermined number of steps from a normal mode zone, the normal mode zone initially starting in a first stage carried-out when an auto-focusing is performed;

carrying out a second stage in the normal mode zone when the first resultant value is smaller than the first threshold value, detecting a second presently-detected focus value by decreasing the electrical current by the first predetermined number of steps, and comparing a second resultant value obtained by subtracting a second previous focus value from the second presently-detected focus value with a second threshold value;

carrying out a third stage when the second resultant value is smaller than the second threshold value, detecting a third presently-detected focus value by finely increasing the electrical current by the first predetermined number of steps, and comparing a third resultant value obtained by subtracting a third previous focus value from the third presently-detected focus value with a third threshold value; and

detecting an optimum focus value when the third resultant value is smaller than the third threshold value.