The minimum mean-squared error (MMSE) linear detector has been proposed to successfully suppress the multiple access interference and mitigate the near-far problem in direct-sequence code-division multiple access communication systems. In the presence of unknown or time-varying channel parameters, the MMSE linear detector can be implemented by the blind Griffiths' algorithm, which uses the desired signal vector instead of a training sequence of symbols for initial adaptation. In this paper, a variable step-size (VSS) Griffiths' algorithm is proposed for accelerating the convergence speed, especially in the presence of strong interference. Numerical results show that the convergence properties of the VSS Griffiths' algorithm are robust against the wide eigenvalue-spread problem of the correlation matrix associated with the received signal vector compared to the Griffiths' algorithm using a fixed step-size.