In our previous work, we developed a quadrotor with a tilting frame using the parallel link mechanism. It can tilt its frame in the pitch direction by driving only one servo motor. However, it has a singularity such that the input torque in the pitch direction equals 0 at ±π/2 tilted state. In this letter, we analyze the Hopf bifurcation of the controlled quadrotor around the singularity and show the stable limit cycle occurs in the pitch direction by simulation and experiments.