The k-μ shadowed distribution is an important generalized fading model in wireless communications, capable of effectively describing composite environments involving multipath clustering, shadowing effects, and non-homogeneous scattering. It plays a key role in channel modeling and parameter estimation for 5G/6G networks. However, traditional parameter estimation methods have significant limitations: maximum likelihood estimation (MLE) relies on numerical iterative optimization, resulting in high computational complexity (O(N2) level), which is unsuitable for real-time applications; the traditional method of moments (MoM), although computationally efficient, faces dual challenges of lacking closed-form solutions and diverging estimation variance when dealing with the k-μ shadowed distribution. Particularly under low signal-to-noise ratio (SNR) or limited sample conditions, higher-order moments are extremely sensitive to noise, causing the mean square error (MSE) to deviate significantly from the theoretical lower bound. To address these issues, this paper proposes an improved method of moment estimation framework based on bias-variance tradeoff: leveraging the nonlinear coupling characteristics of the parameters, initial values are constructed under a small perturbation assumption, and an analytical bias correction factor is introduced to achieve low-complexity explicit parameter estimation. This method significantly reduces estimation variance by introducing a small controllable bias; meanwhile, it derives the biased Cramér-Rao lower bound (Bias-CRLB) as a new performance benchmark to verify the effectiveness and robustness of the estimator. Simulation results demonstrate that the algorithm exhibits excellent convergence under various channel parameter configurations, with the average estimated root mean square error (RMSE) as low as 0.024, validating the accuracy of the theoretical derivation. Compared to traditional iterative estimation algorithms, this method avoids complex numerical search processes, significantly reducing computational complexity, and holds deployment potential in resource-constrained scenarios such as edge computing nodes and low-power Internet of Things terminals. This study innovatively introduces a biased estimation framework into the analysis of the k-μ shadowed distribution, not only extending the parameter estimation methods for complex fading channels but also providing new theoretical support for the design of highly reliable communication systems under low SNR and small-sample environments.