The EMGB solution that will be employed as a thin-shell solution with a normal matter [6] is given by (with Λ = 0) with constants, M =mass and Q =charge. For a black hole solution the inner ( r$_{−}$ ) and event horizons ( r + = r$_{h}$ ) are By employing the solution (14) we determine the surface energy-momentum on the thin- shell, which will play the major role in the perturbation. We shall address this problem in the next section. In order to study the radial perturbations of the wormhole we take the throat radius as a function of the proper time, i.e., a = a ( τ ). Based on the generalized Birkhoff theorem, for r > a ( τ ) the geometry will be given still by (6). For the metric function f ( r ) given in (14) one finds the energy density and pressures as [6] III. RADIAL, LINEAR PERTURBATION OF THE THIN-SHELL WORMHOLE WITH NORMAL MATTER We note that in our notation a ’dot’ denotes derivative with respect to the proper time τ and a ’prime’ implies differentiation with respect to the argument of the function. By a simple substitution one can show that, the conservation equation 5 d dτ ( σa $^{3}$) + p d dτ ( a $^{3}$) = 0 . (19) f ( a ) = 1 + a 2 4 α ( 1 − √ 1 + 8 α a 4 ( 2 M π − Q 2 3 a 2 ) . (18) σ = − S τ = − Δ 4 π [ 3 a − 4 α a 3 ( Δ 2 − 3 ( 1 + ˙ a $^{2}$)) ] , (16) S θ = S φ φ = S ψ ψ = p = 1 4 π [ 2Δ a + ℓ Δ − 4 α a 2 ( ℓ Δ − ℓ Δ ( 1 + ˙ a $^{2}$) − 2¨ a Δ )] , (17) r$_{±}$ = √ M π − α ± [ ( M π − α ) 2 − Q 2 3 ] 1 / 2 . (15) f ( r ) = 1 + r 2 4 α ( 1 − √ 1 + 8 α r 4 ( 2 M π − Q 2 3 r 2 ) ) (14) where ℓ = ¨ a + f $^{′}$( a ) / 2 and Δ = √ f ( a ) + ˙ a 2 in which