Potassium tetratitanate (K2Ti4O9) and Potassium hexatitanate (K2Ti6O13) fibers have been prepared by the slow-cooling calcination process in a temperature range from 125$0^{circ}C$ to 95$0^{circ}C$ using the K2CO3 and TiO2 as the starting materials. Optimum fiber growth conditions have been also investigated by changing the physical parameters, such as calcination time and temperature, and cooling rate. Relatively long K2Ti4O9 fibers ( 1.2mm) have been grown with quite a high aspect ratio (c/a 500)when the starting material with a nominal composition of K2O and TiO2 with 1:4 was calcined at 115$0^{circ}C$ for 4h, and then was slowly cooled to 95$0^{circ}C$ with a rate of 2$0^{circ}C$/h. In case of a K2O.6TiO2 composition, acicular shaped K2Ti6O13 fibers with 20~300${mu}{ extrm}{m}$ long and low aspect ratio (c/a 10~15) have been formed irrespective of the coolign rate. The growth condition of fibers have been discussed based upon the phase diagram of K2O-TiOa2.