In the modern biomedical era of developing nanodevices particularly for the disease detection, fast and precise response is appreciated. Horn shaped double single walled carbon nanotube system (DSWNTS) possess excellent sensing characteristics due to better adsorbing effect. The work here focuses on determination of natural frequency of cantilever type horn shape DSWNTS. As it is already proven fact that such a type is less fragile and more sensitive, noticing its mechanical behavior is the need of time. Here, governing equation of motion pertaining to the dynamic analysis is developed by applying modified couple stress theory using variational principle. The natural frequency is determined and compared with the same of classical theory. The size effect is also discussed. The frequency ratio is more in case of modified couple stress theory particularly with less size effect. This work will be useful in design of low dimension structure for vibration isolation or for mechanical biosensor.