In this paper, an improved self adaptive min-sum decoding algorithm for flexible low-density parity-check (LDPC) code is proposed. In the proposed algorithm, new modifications are incorporated in both the check node and variable node update process to support the irregular LDPC codes. In the check node and variable node update process of the proposed algorithm, an improved min-sum approximation and down scaling factors are adopted. These modifications result in good error correcting performance without increasing the computational complexity. Through simulations the proposed decoding algorithm is shown to exhibit better decoding performance by achieving overall FER and BER coding gain improvement of 0.31 and 0.26 dB respectively.