In this paper, we introduce the concept of weighted hesitant fuzzy set, in which different weights are designed to these possible membership values, and the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. Then we define some basic operations such as union, intersection, complement, multiplication and power operation of weighted hesitant fuzzy elements and weighted hesitant fuzzy sets, discuss their operation properties, and propose the score function and variance function of the weighted hesitant fuzzy element to compare two weighted hesitant fuzzy elements. Furthermore, we present two aggregation operators such as the weighted hesitant fuzzy element weighted averaging(WHFWA) operator and the weighted hesitant fuzzy element weighted geometric(WHFWG) operator to aggregate weighted hesitant fuzzy information, and build the mathematical model of group decision making based on the expert weights(known and unknown). Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.