We report here an ultra-broadband linearly polarized (LP) LP₀₁ LP₁₁ mode converter operating at 1 μm based on a long period fiber grating (LPFG) fabricated in a conventional two-mode fiber (TMF) by a line-focused CO₂ laser. The measured 3 dB bandwidth is about 240 nm, which is the broadest bandwidth for such fiber mode converters. The maximum conversion efficiency between the LP₀₁ and LP₁₁ modes is >99% over the range of 1000 nm to 1085 nm, almost covering the whole emission band of Yb³⁺, which is useful for further power scaling of high-power fiber lasers operating at the 1 μm band.