A gridless sparse beamforming (direction-of-arrival (DOA) estimation) method using gradient-based optimization is presented. The approach minimizes the fit between the sample covariance matrix (SCM) and a reconstructed covariance matrix constrained to contain only a few atoms. This enables analytic derivatives using Wirtinger gradients for efficient optimization. The sensitivity to local minima is mitigated by initializing with optimal DOAs from a user-input-free gridded sparse Bayesian learning. Numerical simulations demonstrate the method provides superior resolution compared to conventional approaches.