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 3ee8e8752445f9fa0"> be the generating set of Sn, where for 038d0ef09931" title="Click to view the MathML source">1≤i≤n−1, 037e3bce61a2a7eef932" title="Click to view the MathML source">si is the adjacent transposition. For a subset J⊆S, let (Sn)J be the parabolic subgroup generated by J , and let 3e6cf431e93" title="Click to view the MathML source">(Sn)J be the set of minimal coset representatives for Sn/(Sn)J. For u≤v∈(Sn)J in the Bruhat order and 3e052589" title="Click to view the MathML source">x∈{q,−1}, let denote the parabolic R-polynomial indexed by u and v . Brenti found a formula for when J=S∖{si}, and obtained an expression for when J=S∖{si−1,si}. In this paper, we provide a formula for , where 036d5f39154e2f92bde731f2746b62" title="Click to view the MathML source">J=S∖{si−2,si−1,si} and i appears after i−1 in v. It should be noted that the condition that i appears after i−1 in v is equivalent to that v is a permutation in 03" class="mathmlsrc">03.gif&_user=111111111&_pii=S0022404916300780&_rdoc=1&_issn=00224049&md5=8b11bd77f007398a8c6407e30f0e37e0" title="Click to view the MathML source">(Sn)S∖{si−2,si}. We also pose a conjecture for , where 0312349c4214" title="Click to view the MathML source">J=S∖{sk,sk+1,…,si} with 1≤k≤i≤n−1 and v is a permutation in (Sn)S∖{sk,si}.