Secure transmission in large-scale MISO systems employing artificial noise (AN) is studied under the per-antenna constant envelope (CE) constraint. Achievable secrecy rate of the per-antenna CE precoding scheme for large-scale MISO is analyzed and compared with that of the matched filter linear precoding. A two-stage per-antenna CE precoding scheme for joint signal-plus-AN transmission is proposed. The first stage determines the per-antenna CE precoding for the information-bearing signal. A properly generated AN using an iteration algorithm is incorporated into the transmit signal in the second stage such that the combined signal-plus-AN satisfies the per-antenna CE constraint and the AN is orthogonal to the user channel. It is shown that compared to conventional per-antenna CE transmission, this joint signal-plus-AN secure transmission scheme does not require additional transmit power. An alternative low-complexity AN generation scheme which uses a separate antenna to cancel the AN leakage to the intended user introduced by randomly generated AN is also proposed.