This study proposes a hybrid intelligence approach based on an extreme gradient boosting regression and genetic algorithm, namely, the XGBR-GA model, incorporating Sentinel-2, Sentinel-1, and ALOS-2 PALSAR-2 data to estimate the mangrove above-ground biomass (AGB), including small and shrub mangrove patches in the Red River Delta biosphere reserve across the northern coast of Vietnam. We used the novel extreme gradient boosting decision tree (XGBR) technique together with genetic algorithm (GA) optimization for feature selection to construct and verify a mangrove AGB model using data from a field survey of 105 sampling plots conducted in November and December of 2018 and incorporated the dual polarimetric (HH and HV) data of the ALOS-2 PALSAR-2 L-band and the Sentinel-2 multispectral data combined with Sentinel-1 (C-band VV and VH) data. We employed the root-mean-square error (RMSE) and coefficient of determination (R2) to evaluate the performance of the proposed model. The capability of the XGBR-GA model was assessed via a comparison with other machine-learning (ML) techniques, i.e., the CatBoost regression (CBR), gradient boosted regression tree (GBRT), support vector regression (SVR), and random forest regression (RFR) models. The XGBR-GA model yielded a promising result (R2 = 0.683, RMSE = 25.08 Mg·ha−1) and outperformed the four other ML models. The XGBR-GA model retrieved a mangrove AGB ranging from 17 Mg·ha−1 to 142 Mg·ha−1 (with an average of 72.47 Mg·ha−1). Therefore, multisource optical and synthetic aperture radar (SAR) combined with the XGBR-GA model can be used to estimate the mangrove AGB in North Vietnam. The effectiveness of the proposed method needs to be further tested and compared to other mangrove ecosystems in the tropics.