In this work, root-finding using the bisection algorithm is proposed to solve the transcendental dispersion relations and evaluate the dispersion curves of ultrasonic-guided waves propagating in an orthotropic composite plate. The implementation of the dispersion relations are accomplished via a coding scheme conducted in the MATLAB software. The obtained phase and group velocity dispersion curves from MATLAB using the in-house developed code are validated with a freely available Dispersion software and found to be in good agreement. Further, qualitative, and quantitative analysis is conducted considering different layers and fiber direction of the composite plate to verify the of accuracy of the obtained results.