Bill Gross says bonds will have a tough period ahead if the Federal Reserve relies on job growth as a critical measure for raising interest rates.

After a Labor Department report today showed that payroll growth surged in December to 292,000, Gross said it appears that the Fed is on track to raise rates three or four times this year, based on statements from policy makers. 

"If the Fed continues to believe jobs are a critical element as opposed to aggregate demand and global growth, bonds have a sad period ahead of them," Gross, the lead manager of the $1.3 billion Janus Global Unconstrained Bond Fund, said in a Bloomberg Radio interview.

The Federal Reserve raised interest rates in December for the first time in almost a decade after a strong year of job growth. Payrolls increased by 2.65 million last year compared with 3.1 million in 2014 — the best back-to-back years for hiring since 1998-99. The central bank is counting on job growth leading to increases in worker pay and inflation.

"The Fed does believe that jobs and the unemployment rate is critical to future inflation over the medium term," Gross said. "So the three or four Fed steps that Stan Fischer and Janet Yellen seem to confirm are probably on track, at least in their verbiage."

Gross said he doesn’t think it’s possible to raise interest rates by 100 basis points in today’s levered global economy, in which the dollar is rising and hurting companies in emerging markets. Bonds will be stable if the Fed only raises interest rates one or two times over next 12 months, said Gross.

In Gross’s monthly investment outlook Thursday, Gross warned that demographics, including the aging of the Baby Boom generation, will lead to slower U.S. growth over the next few decades. "Long-term then, as opposed to currently, think about increasing your asset allocation to the developing world," he wrote.

Gross’ Janus Global Unconstrained Bond Fund rose 0.2 percent in the last 12 months, beating 80 percent of its peers, according to data compiled by Bloomberg.