The exploration of new two-dimensional (2D) allotropes of carbon has attracted great research attention after graphene, but experiment-feasible graphene allotropes with novel properties are still rare. Here, we predict a new allotrope of graphene, named Me-graphene, composed of both sp2- and sp3-hybridized carbon by topological assembly of C-(C3H2)4 molecules. With a transitional ratio of sp2- and sp3-hybridized carbon atoms (12 : 1) between those of graphene (1 : 0) and penta-graphene (2 : 1), Me-graphene has transition properties between those of graphene and penta-graphene, such as energy, band gap, and Poisson's ratio. Unusually, Me-graphene exhibits a near zero Poisson's ratio of from -0.002 to 0.009 in the xy-plane (or called "anepirretic"), different from that of graphene (0.169) and penta-graphene (-0.068). More importantly, the near zero Poisson's ratio behavior remains in a large strain range, being less than ±0.02 for strain from -15% to +3%. Me-graphene possesses an indirect band gap of 2.04 eV, as a transition of graphene (semimetal) and penta-graphene (wide band gap), and turns into a direct-bandgap semiconductor with an enlarged band gap of 2.62 eV under compressive strain. It possesses high hole mobility of 1.60 × 105 cm2 V-1 s-1 at 300 K. Me-Graphene has potential applications in electronic, photoelectric and high-speed mechatronic devices. The transitional properties related to the ratio of sp2- and sp3-hybridized carbon atoms are inspiring for searching for new graphene allotropes with combinational properties.