The method for calculating the non-Markovian full counting statistics (FCS) of electron transport through single molecule devices in the sequential-tunneling regime is developed based on an efficient particle-number-resolved time-convolutionless master equation.It is demonstrated that the non-Markovian effect manifests itself through the quantum coherence of the considered single molecule system and has a dramatic impact on the FCS in the relatively highly coherent quantum systems.The validity of this approach is well illustrated by the serially coupled double quantum dot (QD) and side-coupled double QD molecules.For serially coupled double QD molecule, when the coupling of the QDs system with the incident-electrode is stronger than that with the outgoing-electrode, the non-Markovian effect can induce a strong negative differential conductance and enhance the current noise to super-Poissonian values for the case of a relatively large ratio of the coupling of the QDs system with the incident-electrode to the hopping coupling between the two QDs.While for side-coupled double QD molecule with a relatively highly coherent quantum, the non-Markovian effect can remarkably enhance the super-Poissonian noise, even leading to the transitions of the skewness and kurtosis from small positive to large negative values.