Graphene and fullerene, two types of C allotropes with very different structures and properties, have attracted considerable attention from the scientific community as new forms of carbon for several decades. It will be a great advantage to combine the geometrical features of the two. Herein, we report a series of novel two-dimensional carbon allotropes that possess fullerene-like hollow structures (bubbles) embedded in a graphene sheet. These carbon allotropes are both thermally and dynamically stable. Calculations using hybrid functionals show that these two-dimensional carbon allotropes could be metals or semiconductors depending on the size and the pattern of the bubbles. The band gap can be as large as 1.66 eV. Due to the unique atomic configuration, some bubble-wrap carbons have unusual negative Poisson's ratios. The combination of graphene and fullerenes provides an appealing approach to design carbon-based materials with dexterous properties. For example, the insertion of the metal atoms inside the bubbles may greatly enhance the functions of such materials in photovoltaics and catalysis.