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[en] Highlights: • Be and B decoration of ptC-aBCNNRs have narrower and wider energy gaps, respectively. • Be decoration of ptC-aBCNNRs has strongest third-order NLO respond in THG process. • B decoration of ptC-aBCNNRs has strongest third-order NLO respond in DFWM process. • A giant third-order NLO susceptibility χ(3) of 1 esu is predicted. • ptC-aBCNNRs present large value of nonlinear optical refractive index and great TPA properties. Planar tetracoordinate carbon (ptC) with intriguing planar bond structure has triggered great attentions. In this work, B/Be-terminated decoration form armchair hybridized boron nitride and graphene nanoribbons with ptC structure (ptC-aBCNNRs) are investigated theoretically for third-order nonlinear optical (NLO) response by employing time-dependent density functional theory combined with sum-over-states method. Our calculations reveal Be and B decorated on ptC-aBCNNRs would result in opposite variation of energy gaps, and strongly enhance the NLO response in different third-order NLO processes. The strong third-order NLO response predicted for ptC-aBCNNRs is originated from the charge redistribution induced by ptC structure and hexagonal-BN ribbon insertion.