We describe an approach to statistical parsing with Tree-Wrapping Grammars (TWG). TWG is a tree-rewriting formalism which includes the tree-combination operations of substitution, sisteradjunction and tree-wrapping substitution. TWGs can be extracted from constituency treebanks and aim at representing long distance dependencies (LDDs) in a linguistically adequate way. We present a parsing algorithm for TWGs based on neural supertagging and A * parsing. We extract a TWG for English from the treebanks for Role and Reference Grammar and discuss first parsing results with this grammar.