Reliable wireless communication often requires accurate knowledge of the underlying multipath channels. Numerous measurement campaigns have shown that physical multipath channels tend to exhibit a sparse structure. Conventional blind channel identification (BCI) strategies such as the least squares, which are known to be optimal under the assumption of rich multipath channels, are ill-suited to exploiting the inherent sparse nature of multipath channels. Recently, l1-norm regularized least-squares-type approaches have been proposed to address this problem with a single parameter governing all coefficients, which is equivalent to maximum a posteriori probability estimation with a Laplacian prior for the channel coefficients. Since Laplace prior is not conjugate to the Gaussian likelihood, no closed form of Bayesian inference is possible. Following a different approach, this paper deals with blind channel identification of a single-input multiple-output (SIMO) system based on sparse Bayesian learning (SBL). The inherent sparse nature of wireless multipath channels is exploited by incorporating a transformative cross relation formulation into a general Bayesian framework, in which the filter coefficients are governed by independent scalar parameters. A fast iterative Bayesian inference method is then applied to the proposed model for obtaining sparse solutions, which completely eliminates the need for computationally costly parameter fine tuning, which is necessary in the l1-norm regularization method. Simulation results are provided to demonstrate the superior effectiveness of the proposed channel estimation algorithm over the conventional least squares (LS) scheme as well as the l1-norm regularization method. It is shown that the proposed algorithm exhibits superior estimation performance compared to both LS and l1-norm regularization methods.