Multi-photon Fock states have diverse applications such as optical quantum information processing. For the implementation of quantum information processing, Fock states should be generated within the telecommunication wavelength band, particularly in the C-band (1530-1565 nm). This is because mature optical communication technologies can be leveraged for transmission, manipulation, and detection. Additionally, to achieve high-speed quantum information processing, Fock states should be generated in optical pulses with as short a duration as possible, as this allows embedding lots of information in the time domain. In this paper, we successfully generate picosecond pulsed multi-photon Fock states (single-photon and two-photon states) in the C-band with Wigner negativities for the first time, which are verified by pulsed homodyne tomography. In our experimental setup, we utilize a single-pixel superconducting nanostrip photon-number-resolving detector (SNSPD), which is expected to facilitate the high-rate generation of various quantum states. This capability stems from the high temporal resolution of SNSPDs (several tens of picoseconds in our case and also in general) allowing us to increase the repetition frequency of pulsed light from the conventional MHz range to the GHz range, although in this experiment the repetition frequency is limited to 10 MHz due to the bandwidth of the homodyne detector. Consequently, our experimental setup is anticipated to serve as a prototype of a high-speed optical quantum state generator for ultrafast quantum information processing at telecommunication wavelength.