Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 186; Flight Crew Type 7000
Situational Awareness
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Fuel Issue
Flight Crew Diverted; Flight Crew Landed As Precaution; General Maintenance Action
Aircraft
The incident occurred enroute at FL350. Left center tank fuel pump was MEL inop. We took off with 1800 pounds in center tank. After center tank drained; had approximately a 1700-pound fuel imbalance with right side heavier. We transferred fuel; and had both tanks stable at about 6500 pounds each. Right main fuel tank quantity indicator intermittently went to zero many times at cruise; then remained at zero. We wrote up discrepancy in the logbook; and were in process of sending Maintenance message describing condition when left main fuel tank quantity indicator began to intermittently show zero. While attempting to verify fuel on board in FMC; I noticed the FMC fuel onboard total drop from 10.3 to 4.3 in less than one minute. I verified FMC routing to eliminate a routing discrepancy causing the FMC fuel reading to possibly be erroneous. No discrepancy existed; and the total fuel on board number in the FMC continued to rapidly decrease. Without reliable main fuel tank quantity indicators; and with the FMC fuel quantity rapidly decreasing; I made the decision to initiate a rapid descent; and requested nearest suitable airport from ATC. My concern was a fuel leak; and I had no way of verifying fuel on board. No caution or warning; or low pressure lights illuminated. I flew aircraft; communicated with ATC; and communicated with the Flight Attendants and Passengers; while First Officer prepared landing data and communicated with Dispatch.  We performed an uneventful flaps 40 landing.I feel the main contributing factor in this situation is the aging condition of the 737-Classic series fleet. It is not uncommon to have multiple MELs on these aircraft for major components like fuel pumps and gauges.
B737 Captain reported a loss of fuel quantity indication at FL350 with the FMC showing decreasing fuel. Fearing a possible fuel leak the Captain elected to divert to a suitable alternate.