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We propose a spot-size converter (SSC) by exploiting the high-efficiency mode conversion capability that a long-period grating (LPG) possesses. Our proof-of-concept LPG-based SSC, fabricated with optical polymer material on silicon nitride (Si₃N₄) platform, has a length of &#x223C;700 &#x03BC;m, can improve the coupling efficiency between the LP<italic>^x</italic>₀₁ mode of an ultra-high numerical aperture fiber and the E<italic>^x</italic>₁₁ mode of the Si₃N₄ waveguide from &#x223C;24&#x0025; to &#x223C;33&#x0025; at 1548 nm wavelength, corresponding to 1.4-dB reduction in insertion loss. Therein, the LPG achieves a maximum mode conversion efficiency of 90&#x0025; between the two E<italic>^x</italic>₁₁ modes of the polymer cladding and the Si₃N₄ core. Our proposed SSC provides a new path to achieve low-loss fiber-to-chip coupling.