Charge acceleration during an intense light field application to solids attracts much attention as elementary processes in high-harmonic generation and photoelectron emission. For manipulating such attosecond dynamics of charge, carrier-envelope-phase (CEP: relative phase between carrier oscillation of light field and its envelope function) control has been employed in insulators, nanometal and graphene. In superconducting materials, collective control of charge motion is expected because of its strongly coherent nature of quasi-particles. Here we report that, in a layered organic superconductor, a non-linear petahertz current driven by a single-cycle 6 femtosecond near infrared field shows up as second harmonic generation (SHG), which is in contrast to the common belief that even harmonics are forbidden in the centrosymmetric system. The SHG represents a CEP sensitive nature and an enhancement near the superconducting temperature. The result and its quantum many-body analysis indicate that a polarized current is induced by non-linear acceleration of charge, which is amplified by superconducting fluctuations. This will lead to petahertz functions of superconductors and of strongly correlated systems.