The effects of additive injection including CH2O and H2O2 on the ignition characteristics of a lean primary reference fuel (PRF)/air mixture under homogeneous-charge compression ignition (HCCI) combustion conditions are investigated using 2-D direct numerical simulations (DNSs) with a 116-species reduced chemical mechanism. The 2-D DNSs of HCCI combustion are performed by varying the type and amount of the additives with a pseudo-species model and a compression-heating/expansion-cooling model. It is found that the first-stage and main ignitions are retarded by CH2O addition while the latter is promoted by H2O2 addition. By adjusting the amounts of dual additives, the main ignition can be manipulated to occur at a specific time similar to that with no additives while its mean heat release rate becomes more distributed over time than that with no additives. Combustion mode analysis reveals that a mixed mode of combustion occurs during the late phase of HCCI combustion with CH2O addition or dual additives, while spontaneous ignition mode of combustion is predominant for cases with H2O2 addition or no additives. Displacement speed analysis also verifies that CH2O addition induces deflagration rather than spontaneous ignition at the reaction fronts, which consequently leads to a smooth ignition of the RPF/air mixture. In addition, chemical explosive mode analysis (CEMA) identifies important variables and elementary reactions for low-, intermediate-, and high-temperature chemistries for the ignition of PRF/air mixture with and without additives.