This paper described the method and the result of making a dynamic fiber optic gyrocompass measuring the heading angles of ships by processing the output signal from a constant rotating fiber optic sensor and also showed the measurement to test the performance of our system. Considerig an economical view we designed and ordered a cheap medium grade fiber densors increased not fiber length but the diameter of a fiber sensing loop. The scale factor and noise was 267mV/deg/s and 2 deg/hr/$sqrt{Hz}(1{sigma})$, respectively. We made the dynamic fiber optic gyrocompass by this sensor. We measured the heading angles in an arbitrary direction to evaluate the accuracy of our system and the root mean square error was $0.4^circ$. Moreover, we measured the angles ineach direction of $45^circ$. successive rotation to know whether this system has distoritions in a specific direction or not and the root mean square error in this case was $0.5^circ$.