This paper is concerned with the problem of robust observer design for linear systems with neutral-type time-delays. Delay-independent and delay-dependent conditions are presented to solve the observation/filtering issue under noisy output measurements. Stated as linear matrix inequalities conditions, these sufficient conditions enable the determination of the observer gains that guarantee both asymptotic convergence of the observer in case of noiseless measurements and robust filtering in case of presence of measurements errors. The proposed linear matrix inequality conditions are derived without any major approximation or assumption on the neutral type time-delay system which make the observer design straightforward and less conservative.