In this paper Model Predictive Control (MPC) for SISO LTI system is considered. MPC emanates from dynamic optimisation where a dynamical system is controlled while minimising the associated performance index and satisfying all the constraints. Using current measurement of states (if all states are available for measurement else state observer is used) a predicted plant model is obtained on a prediction horizon (N) and using this predicted plant model we get the predicted performance index which is minimized to get a future control sequence. The first component of the control sequence is used while rest gets discarded and at the next instance the whole process is repeated. In this paper a LTI SISO system is subjected to constraints on both input and output is considered. Simulation results verify the efficacy of the designed algorithm.