This paper aims to discuss inequalities involving extension of Euclidean numerical radius. We obtain a refinement of the inequality shown by Sattari et al. We give an improvement of the inequality presented by Kittaneh for the numerical radius. In fact we show that if T ∈ B(H), then ω 2 (T) ≤ 1 2 T * T + TT * − inf x=1 φ(x), where φ(x) = |T| − |T|x, x 2 + |T * | − |T * |x, x 2 x, x,