In Pedersen’s VSS scheme the secret is embedded in commitments. And the polynomial used is of degree at most (t-1). In strong – (t, n) VSS which based on Pedersen’s scheme that polynomial in verification purpose is public polynomial. The public polynomial in their scheme which acts in verification purpose is not secure. And the secret is secure if the dealer cannot solve the discrete logarithm problem. In our propose scheme we will satisfy the security requirements in strong t-consistency and consider the security on verification polynomial used. We will show in shares verification algorithm the participants can verify that their shares are consistent and the dealer is honest (i.e. the dealer cannot success in distributing incorrect shares even the dealer can solve the discrete logarithm problem.) before start secret reconstruction algorithm. The security strength of the proposed scheme lies in the fact that the shares and all the broadcasted information convey no information about the secret.