Laser-plasma accelerators (LPAs) generate high-quality relativistic electron beams from orders-of-magnitude shorter acceleration distances than conventional radio-frequency technology1–4. Most current LPAs require driver lasers with relativistic intensities and pulse lengths significantly shorter than the plasma wavelength5–7, which severely limits LPA operation and applications. Here, we report a novel parametrically-excited LPA (PEPA) regime based on direct plasma wave excitation, which markedly relaxes the driver laser requirements and exhibits a laser to electron-beam energy conversion efficiency and accelerated charge per laser energy ratio that are unprecedented for gas-phase targets. We experimentally demonstrate highly reproducible generation of mildly relativistic electron bunches with nearly 10 nC of charge from a gas target with ultrahigh accelerating fields of more than 2 TV/m. The LPA operates at near quarter-critical plasma density and uses a driver laser with 37 fs pulse duration (several plasma wavelengths long) and only 120 mJ pulse energy. Our results demonstrate a novel LPA concept operating in a widely unexplored regime that holds the promise for efficient widespread ultracompact high-repetition rate particle accelerators and secondary sources with applications spanning from fundamental research, industry, and medicine to energy sciences.