Walter Wolf Racing was founded for the 1977 season by Canadian oil magnate Walter Wolf, who had previously held a majority stake in Frank Williams Racing Cars before that relationship broke down and Frank Williams departed to establish Williams Grand Prix Engineering. To replace the renamed Hesketh 308C that had served as a stop-gap in 1976, Wolf assembled a design group led by Harvey Postlethwaite, who had come from Hesketh Racing. The resulting WR1 was an immediate success, winning on its debut at the 1977 Argentine Grand Prix with Jody Scheckter.
The WR4 was produced at the close of the 1977 season as the fourth chassis in the Wolf series, incorporating slight adjustments relative to its predecessors — WR1, WR2, and WR3. The WR1 was also remodelled in a similar fashion for use in 1978, meaning the team effectively operated an updated pair alongside the retained WR3.
The WR4's competition career took place almost entirely in 1978, a year in which the Walter Wolf Racing operation faced a steep decline in competitiveness. The advent of ground effect — pioneered most dramatically by the Lotus 78 and 79 — rendered the conventional WR1-family aerodynamics obsolete. Neither the WR4 configuration nor the remodelled WR1 could match the downforce generated by the fully skirted cars emerging from rival teams.
Keke Rosberg drove WR3 and later WR4 as part of a Theodore Racing sub-entry arrangement. He managed to finish just one race in the car, at the 1978 German Grand Prix at Hockenheim. Jody Scheckter, still the team's lead driver, had one more notable moment with the original WR1 at the 1978 Monaco Grand Prix, where he finished on the podium, but this was an exception in an otherwise difficult season for the entire WR1 family of cars.
Halfway through 1978, Walter Wolf Racing introduced the new WR5, which took over the lead role and eventually carried the team's remaining points before the programme wound down.
The Wolf WR4 is historically inseparable from the WR1 family that preceded it, a lineage whose crowning achievement was Scheckter's near-championship 1977 campaign. The WR4 itself, produced as a late-season update and used in a handful of 1978 races, represented the final evolution of that original concept before ground-effect rendered it obsolete. The car's brief life illustrated how rapidly the technical landscape of Formula One shifted in the late 1970s, where a design good enough to win three races in one year could be a backmarker the next. For Keke Rosberg, the WR4 provided limited track time at an early stage of a career that would eventually culminate in the 1982 World Championship.