Relaying is one of the useful techniques to enhance wireless physical-layer security. Existing literature shows that employing full-duplex relay instead of conventional half-duplex relay improves secrecy capacity and secrecy outage probability, but this is at the price of sophisticated implementation. As an alternative, two-path successive relaying has been proposed to emulate operation of full-duplex relay by scheduling a pair of half-duplex relays to assist the source transmission alternately. However, the performance of two-path successive relaying in secrecy communication remains unexplored. This paper proposes a secrecy two-path successive relaying protocol for a scenario with one source, one destination and two half-duplex relays. The relays operate alternately in a time division mode to forward messages continuously from source to destination in the presence of an eavesdropper. Analytical results reveal that the use of two half-duplex relays in the proposed scheme contributes towards a quadratically lower probability of interception compared to full-duplex relaying. Numerical simulations show that the proposed protocol achieves the ergodic achievable secrecy rate of full-duplex relaying while delivering the lowest probability of interception and secrecy outage probability compared to the existing half duplex relaying, full duplex relaying and full duplex jamming schemes.