Motivated by practical applications from social influence and viral marketing, this work studies the problem of Influence Maximization with Fairness Allocation Constraint, which aims to find a set of k users from groups in a social network with maximal influence spread so that the number of selected uses in each group does not exceed the group budget. We propose an efficient and scalable approximation algorithm that returns an approximation ratio of \(1/2-\epsilon \) and takes \(O((m+\log (\frac{k}{\epsilon }))\frac{n}{\epsilon ^2}(k \log n+\log (\frac{1}{\delta })))\) time complexity, where \(\epsilon , \delta \) are constants, n is the number of uses and m is the number of links. Besides theoretical results, extensive experiments conducted on real social networks show that our algorithm provides better solutions than cutting-edge methods.