The paper deals with design of high-gain Observer for nonlinear system with delayed output measurements and bounded disturbances. The new structure of the proposed observer exhibits good performance in term of allowing a higher MAVTD (Maximum Allowable Value of the Time-Delay) comparing to the existing works, where the MAVTD is limited due to the high value of the high-gain parameter. Based on LMI technique and using Lyapunov-Krasovskii functional, an explicit relation between MAVTD and the LMI tuning parameters is deduced from the stability analysis of the proposed observer. The efficiency of the proposed structure is illustrated through an application to a Quadrotor UAV and a comparison with standard and cascade high-gain observers is performed.