  We construct analytical models to study the critical phenomena in
gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We
first use the cut-and-paste technique to match the conformally flat solution
($c=0$ ) onto an outgoing Vaidya solution. To guarantee the continuity of the
metric and the extrinsic curvature, we prove that the two solutions must be
joined at a null hypersurface and the metric function in Vaidya spacetime must
satisfy some constraints. We find that the mass of the black hole in the
resulting spacetime takes the form $M\propto (p-p^*)^\gamma$, where the
critical exponent $\gamma$ is equal to $0.5$. For the case $c\neq 0$, we show
that the scalar field must be joined onto two pieces of Vaidya spacetimes to
avoid a naked singularity. We also derive the power-law mass formula with
$\gamma=0.5$. Compared with previous analytical models constructed from a
different scalar field with continuous self-similarity, we obtain the same
value of $\gamma$. However, we show that the solution with $c\neq 0$ is not
self-similar. Therefore, we provide a rare example that a scalar field without
self-similarity also possesses the features of critical collapse.
