With low Peak-to-Average Power Ratio (PAPR), Single Carrier - Frequency Division Multiple Access (SCFDMA) is adopted by 3GPP to be the uplink access method of the LTE system. SC-FDMA allocates continuous Resource Blocks (RBs) to each subscriber to reduce PAPR. However, the continuous RB allocation degrades the flexibility in resource allocation. How to efficiently allocate radio resource in the SCFDMA scheme has been a critical issue. This paper proposes a scheduling algorithm concerning user satisfaction in LTE uplink radio resource allocation. The proposed algorithm is a generalization and an improvement of the well-known Mean Enhanced Greedy (MEG) scheduling algorithm. The simulation results show that the proposed algorithm achieves not only higher user satisfaction degree but also better fairness between subscribers than the MEG scheduling algorithm and a related algorithm, called the Recursive Maximum Expansion (RME) algorithm, no matter the desired uplink transmission rates among subscribers are the same or not.