Frequent itemset mining in uncertain transaction databases semantically and computationally differs from traditional techniques applied on standard (certain) transaction databases. Uncertain transaction databases consist of sets of existentially uncertain items. The uncertainty of items in transactions makes traditional techniques inapplicable. In this paper, we tackle the problem of finding probabilistic frequent itemsets based on possible world semantics. In this context, an itemset X is called frequent if the probability that X occurs in at least minSup transactions is above a given threshold. We make the following contributions: We propose the first probabilistic FP-Growth algorithm (ProFP-Growth) and associated probabilistic FP-Tree (ProFP-Tree), which we use to mine all probabilistic frequent itemsets in uncertain transaction databases without candidate generation. In addition, we propose an efficient technique to compute the support probability distribution of an itemset in linear time using the concept of generating functions. An extensive experimental section evaluates the our proposed techniques and shows that our ProFP-Growth approach is significantly faster than the current state-of-the-art algorithm.