The diagonal relationship between beryllium and aluminum and the isoelectronic relationship between BeH unit and Al atom were utilized to design a new series ppC- or quasi-ppC-containing species C5v CBe5H5(+), Cs CBe5H4, C2v CBe5H3(-), and C2v CBe5H2(2-) by replacing the Al atoms in previously reported global minima planar pentacoordinate carbon (ppC) species D5h CAl5(+), C2v CAl4Be, C2v CAl3Be2(-), and C2v CAl2Be3(2-) with BeH units. The three-center two-electron (3c-2e) bonds formed between Be and bridging H atoms were crucial for the stabilization of these ppC species. The natural bond orbital (NBO) and adaptive natural density partitioning (AdNDP) analyses revealed that the central ppCs or quasi-ppCs possess the stable eight electron-shell structures. The AdNDP analyses also disclosed that these species are all 6σ+2π double-aromatic in nature. The aromaticity was proved by the calculated negative nucleus-independent chemical shifts (NICS) values. DFT and high-level CCSD(T) calculations revealed that these ppC- or quasi-ppC species are the global minimum or competitive low-lying local minimum (Cs CBe5H4) on their potential energy surfaces. The Born-Oppenheimer molecular dynamic (BOMD) simulations revealed that the H atoms in C2v CBe5H3(-) and C2v CBe5H2(2-) can easily rotate around the CBe5 cores and the structure of quasi-planar C5v CBe5H5(+) will become the planar structure at room temperature; however, these interesting dynamic behaviors did not indicate the kinetic instability as the basic ppC structures were maintained during the simulations. Therefore, it would be potentially possible to realize these interesting ppC- or quasi-ppc-species in future experiments.