Parabolic R-polynomials were introduced by Deodhar as parabolic analogues of ordinary R-polynomials defined by Kazhdan and Lusztig. In this paper, we are concerned with the computation of parabolic R -polynomials for the symmetric group. Let Sn be the symmetric group on {1,2,…,n}, and let e4443ee8e8752445f9fa0"> be the generating set of Sn, where for 931" title="Click to view the MathML source">1≤i≤n−1, e61a2a7eef932" title="Click to view the MathML source">si is the adjacent transposition. For a subset a384fd342a67cad6a5" title="Click to view the MathML source">J⊆S, let e6f697f546828c6f758" title="Click to view the MathML source">(Sn)J be the parabolic subgroup generated by J , and let 939baf69187fd7813e6cf431e93" title="Click to view the MathML source">(Sn)J be the set of minimal coset representatives for Sn/(Sn)J. For e611642a1f7b5f38" title="Click to view the MathML source">u≤v∈(Sn)J in the Bruhat order and x∈{q,−1}, let 9306b58c8fcac8a76e461543c2f6456"> denote the parabolic R-polynomial indexed by u and v . Brenti found a formula for 9306b58c8fcac8a76e461543c2f6456"> when J=S∖{si}, and obtained an expression for 9306b58c8fcac8a76e461543c2f6456"> when 93c3a846c30" title="Click to view the MathML source">J=S∖{si−1,si}. In this paper, we provide a formula for 9306b58c8fcac8a76e461543c2f6456">, where bde731f2746b62" title="Click to view the MathML source">J=S∖{si−2,si−1,si} and i appears after a3df6d8c5a241c5e3" title="Click to view the MathML source">i−1 in v. It should be noted that the condition that i appears after a3df6d8c5a241c5e3" title="Click to view the MathML source">i−1 in v is equivalent to that v is a permutation in bd77f007398a8c6407e30f0e37e0" title="Click to view the MathML source">(Sn)S∖{si−2,si}. We also pose a conjecture for 9306b58c8fcac8a76e461543c2f6456">, where J=S∖{sk,sk+1,…,si} with 1≤k≤i≤n−1 and v is a permutation in bd72a4a3c29196cb8bf4f62f83f5c" title="Click to view the MathML source">(Sn)S∖{sk,si}.