The monocular structured light measurement system is widely applied across various fields due to its simple structure, low cost, and extensive measurement range. However, measurement accuracy can be affected by noise, non-linear intensity variations, variations in object surface reflectance, and calibration precision, leading to unstable or inaccurate results. Traditional filtering methods are limited in effectively addressing complex noise and non-linear issues, and phase-to-height calibration often depends on high-precision motion platforms, which increases system costs, complexity, and calibration uncertainty. To address these challenges, this paper proposes a neural network-based approach for monocular structured light measurement. An iterative denoising algorithm based on a denoising autoencoder (DAE) is developed for phase-shift fringe images. By optimizing the iteration count, denoised phase-shift fringes are regenerated to de noise to reduce image noise and enhance phase computation accuracy effectively. Additionally, leveraging the high-precision absolute phase calculated from the denoised phase-shift fringe images, a multilayer feedforward neural network (FNN) algorithm is proposed for absolute phase-to-height calibration. This method directly maps the phase-to-height relationship, integrating both intrinsic and extrinsic camera parameters to achieve high-precision calibration without requiring a high-precision motion platform. Consequently, it significantly mitigates errors related to the motion platform and reduces operational errors during calibration. The DAE enhances the quality of phase images, providing more precise input for the FNN calibration and further improving measurement accuracy. Experimental results demonstrate that the proposed method achieves effective 3D reconstruction from low-quality phase-shift fringes and maintains robust performance when measuring objects with varying reflectances.