We first anlayze the conditions under which a matrix obtained by
reducing the $2^n \times 2^n$ polarizing matrix proposed by Ar{\i}kan becomes a
polarizing matrix supporting a polar code of a given length. We then propose a
method to construct length-compatible polar codes in a suboptimal way by
codeword-puncturing and information-refreezing. They have low encoding
and decoding complexity since they can be encoded and decoded similar to
a polar code of length $2^n$. Numerical results show that length-compatible
polar codes designed by the proposed method provide a performance gain of about
1.0-5.0 dB over those obtained by random puncturing with successive cancellation
decoding.