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This chapter utilizes a numerical forward-backward stochastic differential equations (FBSDEs) approach for pricing American options under the Heston model. An advantage of the Heston model is the ability to consider the correlation between the underlying asset and its volatility. The chapter introduces the FBSDEs, briefly mentions one well-known numerical scheme to solve BSDEs and shows a derivation of the BSDE-Θ numerical schemes for the Heston model. The scheme provides a way to approximate the solution and the hedge ratios. The chapter focuses on deriving the BSDE numerical scheme for the Heston BSDE under the risk-neutral measure. It presents numerical experimental studies that focus on American put options under the Heston model using the proposed BSDE-Θ scheme. The scheme exhibits good accuracy, particularly for in-the-money options, and is robust to parameter choices and basis functions. Despite violating the Feller condition, the BSDE-? scheme still demonstrated high accuracy.