This paper proposes a new twist technique and then shows some necessary conditions for prime order curves in the form y^2=x^3+a. Then, by combining x-twist and y-twist, we consider six elliptic curves. For these six elliptic curves, when the characteristic p of the definition field F_q satisfies that p>3 and 3|(p-1), we show that it is possible for only two elliptic curves among the six curves defined over F_q, q=p^<2^i3^j> to have prime orders, where i, j are non-negative integers. Then, we show an example of prime order curve. After that, compared to the complex multiplication method, we evaluate the performance of the proposed method.