A cylindrical-type drift chamber consists of an appropriate array of cylindrical single wire proportional counters and has a simple structure. It is shown that a quadratic function reproduced the space-time relationship in the cylindrical-type drift chamber filled with PR gas (Argon:Methane = 90:10). The difference in the drift times in pair-cells is simply converted into the incident position of charged particles perpendicular to the anode wire using the quadratic function of the space-time relationship. Furthermore, the quadratic function improves the position resolution. A backgammon pattern is employed for the cathode pad of the cylindrical drift chamber. The cylindrical drift cell with a backgammon-shaped cathode pad gives the position resolution along the anode wire. The position resolution in one sigma along the anode wire is obtained to be 1.7 mm on average. The cylindrical-type drift chamber with backgammon-shaped cathode pad may be applied to a two-dimensional position sensitive detector with a compact structure and simple signal-processing electronics.