This work formulates and implements the phaseless auxiliary-field quantum Monte Carlo method in the Hartree-Fock-Bogoliubov (HFB) manifold for systems with strong pairing correlations. HFB walkers are represented in both the product-state and Thouless forms with respect to a flexible reference vacuum, with explicit expressions for the corresponding normalization factors in terms of the representation matrices. In addition, the stochastic gauge formalism is extended from the Slater determinant manifold to the HFB framework, providing additional flexibility in controlling stochastic fluctuations. Benchmark calculations for the Richardson model demonstrate the accuracy and numerical stability of the method.