This paper proposes a new theory and design method for a class of recombination nonuniform filter banks (RNFBs) with linear phase (LP) filters. In a uniform filter bank (FB), consecutive channels are merged by sets of transmultiplexers (TMUXs) to realize a nonuniform FB. RNFBs with LP analysis/synthesis filters are of great interest because the analysis filters for the partially reconstructed signals, through merging, are LP and hence less phase distortions are introduced to the desired signals. We analyze the spectrum supports of the analysis filters of these LP RNFBs. The conditions on the uniform FB and recombination TMUXs of an LP RNFB with good frequency characteristics are determined. These conditions are relatively simple to be satisfied and the uniform FB and recombination TMUXs can be designed separately without much degradation in performance. This allows dynamically recombination of different number of channels in the original uniform FB to give a flexible and time-varying frequency partitioning. Using these results, a method for designing a class of near-perfect-reconstruction (NPR) LP RNFBs with cosine roll-off transition band using the REMEZ algorithm is proposed. A design example is given to show that LP RNFBs with good frequency responses and reasonably low reconstruction errors can be achieved.