The photoinduced transition from the charge-density-wave (CDW) phase to the metallic phase in low-dimensional ladder-type cuprate Sr14Cu24O41 was investigated in terms of femtosecond time-resolved reflection spectroscopy. Following the melting of the CDW order just after photoexcitation, a Drude-like metallic state was formed with a large optical response and maintained for more than 50 ps. The Drude weight increased with increasing fluence with threshold behavior as a result of the cooperative interactions in the CDW domains and reached the value of the Drude weight in the hole-doped metallic compound of Sr4Ca10Cu24O41. These results indicate the photoinduced formation of a similar metallic state driven by hole doping