The spin torque nano-oscillator (STNO), a nanosize microwave signal generator, have caught the attention of a number of researchers due to its obvious advantages. Recently a chiral bulk material with twisted skyrmion has been discovered in studies with different helicity degrees. In this work, we design a new STNO based on twisted skyrmion existing in free layers of magnetic tunnel junction (MTJ) structure. We first investigate the effect of the magnetic moment of fixed layer on the twisted skyrmion and frequency of STNO. Although the magnetic moment of fixed layer does not affect the state of the twisted skyrmion but affects the precession frequency of STNO. Later, the current, external magnetic field and DMI strength are changed to regulate the oscillation frequency of STNO. Our result may be favourable for the design of new twisted skyrmion-based spin torque nano-oscillator.