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This paper presents a noniterative weighted-least-squares (WLS) method for designing allpass variable fractional-delay (VFD) digital filters. After expressing each coefficient of an allpass VFD filter as a polynomial of the VFD parameter p, we develop a noniterative technique for finding the optimal polynomial coefficients, and show that the allpass VFD filter design problem can be efficiently solved without using any iterative procedure while a closed-form solution can be easily obtained through solving a matrix equation. Compared with the existing iterative WLS method that solves a series of approximately linearized WLS minimization problems, the proposed noniterative one can yield much better design results with significantly reduced computational complexity. Moreover, the new WLS method does not involve any convergence issue.