An approximation algorithm for random K-SAT formulas (MAX-R-KSAT) is herein discussed. The proposed algorithm is similar to the unit clause with majority rule algorithm studied in [Franco et all 1986] for the random 3-SAT problem. The results obtained improve the 9/8-approximation given in [De la Vega et all 2002] for MAX-R-3SAT to a 10/9.5-approximation. The new approximation ratio is achieved by using a better algorithm than the one proposed in [De la Vega et all 2002], along with a new upper bound on the maximum number of clauses that can be satisfied in a random K-SAT formula [Achlioptas et all 2003].