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The prototype of L-type ferrimagnets (L-FiM) Fe₂(MoO₄)₃ was synthesized. It displayed a magnetic ordering at T_N1 ~12K, which is characterized by magnetic susceptibility (χ), specific heat capacity (C_p), and dielectric anomaly (ε') under the magnetic field 0≤H≤7T. Applying the magnetic field (H) induced an additional magnetic phase transition below T_N1, denoted as T_N2, along with a malleable ferroelectric polarization (P) appeared with controllable parameters of H and temperature (T) below T_N2. Consequently, a comprehensive phase diagram in the H-T space was established for spin-induced type-II multiferroics. Unlike traditional multiferroics, where a critical field-induced spin-flip P is observed, these multiferroic characteristics exhibit an exceptional nature. The unique behavior may arise from the intricate interplay of T- and H-dependent spin and lattice structures. Hence, a conceptual representation suggests H-induced potential variation in lattice symmetry and conical spin arrangement. These findings may introduce a novel mechanism for multiferroicity, necessitating theoretical and experimental investigations to understand this peculiar phenomenon comprehensively.