Indoor localization is becoming critical to empower Internet of Things for various applications, such as asset tracking, geolocation, and smart cities. Wi-Fi-based indoor localization using received signal strength (RSS) has drawn much attention over the past decade because it does not require extra infrastructure and specialized hardware. It is well known that the localization accuracy using RSS is rather susceptible to the changing environment. Localization by fusing multiple fingerprint functions of RSS is a promising strategy to overcome the above drawback. However, the existing fusion techniques cannot make full use of the intrinsic complementarity among multiple fingerprint functions. It also fails to exploit the knowledge obtained in the offline phase and thus shows low accuracy in the complex environment. This paper proposes a knowledge aided adaptive localization (KAAL) approach by using a global fusion profile (GFP) to mitigate the above shortcomings. First, we propose a GFP construction algorithm by minimizing position errors over all fingerprint functions with weight constraints in the offline phase. Based on the knowledge from GFP and the trained multiple fingerprint models, we then derive two KAAL algorithms, namely, multiple function averaging and optimal function selection, to achieve highly accurate localization results. Experimental results demonstrate that our proposed localization approach is superior to the existing methods both in simulated and real environments.