  The gravitational collapse of a massless scalar field with a self-interaction
term $\lambda\phi^4$ in anti-de Sitter space is investigated. We numerically
investigate the effect of the self-interaction term on the critical amplitudes,
forming time of apparent horizon, stable island and energy transformation. The
results show that a positive $\lambda$ suppresses the formation of black hole,
while a negative $\lambda$ enhances the process. We define two susceptibilities
to characterize the effect of the self-interaction on the black hole formation,
and find that near the critical amplitude, there exists a universal scaling
relation with the critical exponent $\alpha \approx 0.74$ for the time of black
hole formation.
