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In order to solve the problem of broadband omnidirectional acoustic scattering computing for underwater elastic object, broadband acoustic scattering model of underwater elastic object is presented combining Finite-Difference Time-Domain (FDTD) method and the relation between scattering wave spectrum and form function. We simulated broadband acoustic scattering characteristic of elastic aluminum sphere using this method, and compared the result with the corresponding analytic solution, and they were in good agreement. Furthermore, we computed non-backscattering broadband characteristics, which were very difficult to gain using other methods, including bistatic angle 45 degree and 90 degree, and compared and analyzed them. The results showed that their formant position, vibration amplitude and resonance period existed distinct difference, that was to say, with the changing of bistatic angle, frequency domain scattering characteristic of the object brought great difference.