The daily's advice comes only days ahead of Modi's official visit to China this week. It describes the Indian leader as pragmatic rather than a visionary.
The Global Times is known for its sharp views on India.
Calling for both China and India to not only strengthen mutual political trust, but also stick to a series of agreed principles and match their rhetoric with action, it stated: "In light of this, Modi should no longer visit the disputed border region in pursuit of his own political interests, nor should he deliver any remarks that infringe on the consensus on bilateral ties."
"Meanwhile, the Indian government should completely stop supporting the Dalai Lama, and stop making the Tibetan issue a stumbling block to the Sino-Indian relationship," it said.
According to the article, written by Hu Zhiyong of the Institute of International Relations at the Shanghai Academy of Social Sciences, the Indian prime minister has been "playing little tricks" over the border issue "hoping to boost his domestic prestige while increasing his leverage in negotiations with China".
It said that the ball was now in India's court to boost bilateral relations.
"Fostering close ties with India, China's largest neighbor in South Asia, is of great importance to China's perimeter security and stability," Hu wrote.
It also stated that Modi's diplomatic initiatives across the world ever since he assumed office showed that he was pragmatic rather than a visionary.
"Ever since Modi assumed office, he has taken the initiative to actively develop India's relationships with Japan, the US, and European countries in no time, in order to promote the country's poor infrastructure construction and economic development. But his diplomatic moves last year have proven that he is a pragmatist, rather than a visionary."
The writer also underlined the need for people-to-people and cultural exchanges for deepening bilateral relations but said that the Indian elites' "blind arrogance" was not helping matters.
"Due to the Indian elites' blind arrogance and confidence in their democracy, and the inferiority of its ordinary people, very few Indians are able to treat Sino-Indian relations accurately, objectively and rationally. Worse, some Indian media have been irresponsibly exaggerating the conflicts between the two sides, adding fuel to the hostility among the public."
Dwelling on bilateral trade, the article said that "despite the fact that China has already become India's largest trading partner, India's trade deficit with China keeps rising sharply".
"New Delhi is reluctant to admit the widening trade gap is its own fault, nor is it willing to examine its own economic structure and the quality of its exports to China. Instead, it has been repeatedly accusing or directing its anger at China," Hu wrote.
"The Indian government should loosen up on the limits of cross-border trade with China, reduce the trade deficit, improve the efficiency of government administrations, and relax the visa restrictions, in order to attract more Chinese companies to invest in India."
Calling for deepening of bilateral relations through concerted efforts by politicians from both sides, it said: "Modi should seize the chance of his China visit to enhance bilateral cooperation."