Web texts are an important data source for constructing and completing a large-scale knowledge graph that contains a great deal of ubiquitous geographic information. However, the extensive sources, casual expression, and dynamic nature of web texts, as well as the varied quality of implicit geo-information bring great challenges such as multi-level evaluation objects, unclear quality dimensions, diversified evaluation indicators, difficult access to deep-seated indicators, and diversified evaluation methods in the process of geographic information quality assessment. Therefore, a Quality Assessment Framework for implicit Geographic Information from Web Texts (QAF-GIWT) is proposed in this study. The QAF-GIWT is oriented to the process of acquiring geographic information from web texts and defines three levels of quality evaluation objects, i.e., data source level, data item level, and dataset level. The data source level contains websites and web pages, the data item level includes the triplet-formed information extracted from the webpage, and the dataset level is the information aggregated into a Geographic Knowledge Graph (GeoKG). The QAF-GIWT defines four quality dimensions including relevance, novelty, reliability, and integrity, and proposes the corresponding quantitative evaluation indicators for different level evaluation objects including Cell Geographic Semantic Ratio (CGSR), Geographic Semantic Ratio (GSR), Average Geographic Information Ratio (AGIR), Geographic Information Ratio(GIR), Event Time Length, Triplet Existence, Publish Time, Time Validation, Domain Name Time Length, Update Frequency, Average Freshness, Comprehensive Ranking, Category Ranking, Daily Page Visit, Daily User Visit, User Attention, Picture Number, Word Number, Geographic Entities Ratio (GER), Window's Geo-Information Ratio (GIWR), Triplet Missing Rate, Event Information Missing Rate, Relation Missing Rate, Attribute Missing Rate, Location Missing Rate, Relation Redundancy, Attribute Redundancy, etc. It systematically summarizes the characteristics and applicability of the indicator calculation, indicator synthesis, and quality prediction methods involved in the quality evaluation process. Among them, with the help of natural language processing technology and corresponding quality indicator calculation methods, quality indicators are newly constructed from the deep mining of the web texts including CGSR, GSR, AVGIR, GIR, GIWR, GER, etc. In our experiment, the QAF-GIWT framework was designed to adapt to the characteristics of various types of websites e.g., Mafengwo. Aiming at the comprehensive evaluation of multi-level quality indicators, the analytic hierarchy process was used for comprehensive reliability evaluation. Our experiment verified the effectiveness of the QAF-GIWT framework. The QAF-GIWT provides a systematic scheme including quality dimensions, quality indicators, and quality assessment methods for the quality evaluation of geographic information extracted from massive, heterogeneous, and dynamic web texts. The proposed QAF-GIWT can assist in the screening of data sources and filtering of acquired information, greatly reducing the complexity of information acquisition and the redundancy of data storage, and assisting the quality control process of the acquisition of geographic information from web texts.