A single numerical model as integrator of initial value problems of multi-order (1st, 2nd and 3rd) ordinary differential equations is introduced. Utilizing Chebyshev polynomials as the trial function, the method is formulated firstly, by obtaining the continuous form of the proposed scheme via collocation technique and later, arrange in a block-by-block manner as numerical integrator of multi-order ODEs. The convergence properties are investigated and it's established that the proposed method is convergent. A comparison of the problems solved with the new method and existing methods shows that the new method outperformed better than existing methods in terms of accuracy.