The $H_2Ge=Ge:$ and its derivatives ($X_2Ge=Ge:$, X = H, Me, F, Cl, Br, Ph, Ar${ldots}{ldots}$) is a new species. Its cycloaddition reactions is a new area for the study of germylene chemistry. The mechanism of the cycloaddition reaction between singlet state Cl2Ge=Ge: and formaldehyde has been investigated with CCSD(T)//MP2/$6-31G^*$ method. From the potential energy profile, it could be predicted that the reaction has only one dominant reaction pathway. The reaction rule presented is that the two reactants first form a fourmembered Ge-heterocyclic ring germylene through the [2+2] cycloaddition reaction. Because of the 4p unoccupied orbital of Ge: atom in the four-membered Ge-heterocyclic ring germylene and the ${pi}$ orbital of formaldehyde forming a ${pi}{ ightarrow}p$ donor-acceptor bond, the four-membered Ge-heterocyclic ring germylene further combines with formaldehyde to form an intermediate. Because the Ge: atom in intermediate hybridizes to an $sp^3$ hybrid orbital after transition state, then, intermediate isomerizes to a spiro-Ge-heterocyclic ring compound via a transition state. The research result indicates the laws of cycloaddition reaction between $H_2Ge=Ge:$ and formaldehyde, and laid the theory foundation of the cycloaddition reaction between $H_2Ge=Ge:$ and its derivatives ($X_2Ge=Ge:$, X = H, Me, F, Cl, Br, Ph, Ar${ldots}{ldots}$) and asymmetric ${pi}$-bonded compounds, which is significant for the synthesis of small-ring and spiro-Ge-heterocyclic compounds. The study extends research area and enriches the research content of germylene chemistry.