  We develop the concept of quasi-phasematching (QPM) in the recently proposed
traveling-wave Josephson parametric amplifier (TWJPA) with three wave mixing
(3WM). The amplifier is based on a ladder transmission line consisting of
flux-biased radio-frequency SQUIDs possessing non-centrosymmetric nonlinearity
of $\chi^{(2)}$-type. Due to design with periodically inverted groups of
SQUIDs, giving reversal of sign of this nonlinearity, QPM in 3WM process,
$\omega_p=\omega_s+\omega_i$, for pump ($\omega_p$), signal ($\omega_s$), and
idler ($\omega_i$) frequency is achieved. Modeling shows that the TWJPA
bandwidth is sufficiently large (ca. $0.4\omega_p$) and flat, while propagating
unwanted modes, including $\omega_{2p}=2\omega_p$, $\omega_+=\omega_p
+\omega_s$, $\omega_- = 2\omega_p - \omega_s$, etc., is suppressed with the
help of engineered dispersion.
